During the game, you will find that you receive wallpapers for your 'real' computer when certain events are triggered. Here is a list of the current possible wallpapers that you can unlock.
There are currently 155 wallpapers available to unlock. They might not appear even if you fulfill the requirements; no one knows why.
The wallpapers will be displayed by number listed on the game and will have the details about where they're found next to them.
Note: Those marked with "Random Occurrence" are either unknown as to when they appear, or appear depending on how far you are through the game.
#2 - After first clicking on the Picture icon in the Tools section on your computer
#3 - "Dream Sheep" - After sleeping 3 times
#4 - "Blue Passage" - When you first enter the Hand Hub
#5 - "Buddha" - When you activate the Buddha Rave event in Marijuana Goddess World
#6 - "Dot Urotsuki" - After collecting 5 effects (including the instructions)
#7 - "OG3 Dance" - When you interact with the painting of the same image in the Art Gallery
#8 - "The Mysterious World" - When you interact with the painting of the same image in the Art Gallery
#9 - "heart256" - After looking at the fourth book from Urotsuki's left on the second bookcase in the Library
#10 - "Remote Island" - After getting the Fairy effect
#11 - "2." - Random occurrence
#12 - "Crocodile Dog" - After going to the "Green Monster Party" in Garden World
#13 - "Fairytale 11" - When you first enter Theatre World
#14 - "Alley" - When you first enter Japan Town
#15 - "Rainbow" - After getting the Rainbow effect
#16 - "Japanese Urotsuki" - After sleeping 10 times
#17 - "Master" - When you first enter the Underground Bar
#18 - "Sky With A Rainbow" - When you use the Rainbow effect at the Snowy Pipe Organ
#19 - "TV Rodeo" - When you first enter room with the purple wavy lines on the floor at the Underwater Amusement Park
#20 - "Dancer" - When triggering Odorika's full screen dance event
#21 - "Effects Festival" - When you collect 10 effects
#22 - "Provost" - When encountering the Commando and Provost-san when the submarine is not open
#23 - "Childbirth" - After encountering Mother in the Urotsuki's Dream Apartments
#24 - "Scars" - When you interact with the giant mannequin in Nail World
#25 - "Signs" - When you first enter Sign World
#26 - “Space” - After chainsawing Tapir-San's back to get into Space
#27 - "White Twintails" - After getting the Twintails effect
#28 - "Octopus Man" - After using the Fairy effect on Tako Otoko
#29 - "Painter" - After entering the first painting you see in the Art Gallery after going through the easel
#30 - "Giant Squid" - When you first enter Atlantis from the grand piano at the Snowy Pipe Organ
#31 - "Order" - When you swim down the road leading to the Underwater Amusement Park
#32 - "Green Juice" - After interacting with Cripple-tan
#33 - "Boy 1" - After getting the Boy effect
#34 - "Comic Urotsuki" - Random occurrence
#35 - "Gakuran" - After getting the School Boy effect
#36 - "Spring" - After getting the Spring effect
#37 - "TV" - When you enter Urotsuki's Dream Apartments and turn on the TV
#38 - "Heart" - After entering Valentine Land from Sign World
#39 - "Chocolate" - When you first enter Chocolate World
#40 - "Park" - After chainsawing the sane Shadow Woman in Forest World, going underground and then emerging
#41 - “Doppelganger” - When using the glasses effect on the nighttime ledge in Day & Night Towers
#42 - “Headless Woman” - When you interact with the Music Box Woman found in Nail World
#43 - "Director's Daughter" - Random occurence
#44 - "Even Without Support" - When you interact with the painting of the same image in the Art Gallery
#45 - “Hourglass Desert” - When you first enter Sand Desert Land
#46 - “Confinement” - When you first enter the clown's dungeon in the Underwater Amusement Park
#47 - “Those Who Wait” - After interacting with the Boy on the Bench in the Blue Forest
#48 - “Twins” - After interacting with the Beret Twins
#49 - “inu 1” - When you first enter Teddy Bear Land
#50 - “Megusuri & Hako-ko” - After interacting with Megusuri Uri in the Eyeball Shop
#51 - "Itetsuki" - After trying on the winter gear in the Dressing Room (You must have completed the Plated Snow Country minigame)
#52 - “Sweets” - After using the Cake effect on Sweets Musume
#53 - “Musician & Cat” - After meeting Elvis Masada
#54 - “Cake-chan” - After getting the Cake effect
#55 - “Zerisan” - Random occurrence
#56 - “Mini Game (↑V↑)” - After completing the ↑V↑ minigame
#57 - “Incubation” - After coming across the creatures in tanks at the Power Plant
#58 - "Silhouette" - When you first enter Monochrome Street
#59 - "Uboa" - When encountering Dogboa
#60 - "UFO" - After getting abducted from the Apartments
#61 - "Fox" - When encountering Yukata
#62 - "Mars" - After interacting with the Blue Crying Man after the Zalgo event
#63 - "Twintails & Black Telephone" - After getting the Twintails effect
#64 - "Reading Theatre" - When using the Telephone effect on Oni Musume while she is reading
#65 - "Sweets Musume" - After using the Cake effect on Sweets Musume
#66 - "Don't Watch" - When you climb up the ladder to Tapir-San's Place
#67 - "Present/Past" - After viewing the lonely Urotsuki event in the Underwater Amusement Park
#68 - "Dreams & Reality" - After sleeping 30 times
#69 - "My Real Studies" - After activating the cloning machine in Toy World
#70 - "Killing Mirror in a Dream" - After chainsawing your "reflection" in a room in Day & Night Towers
#71 - "Monmonzu" - When communicating with the grey NPCs in Marijuana Goddess World
#72 - "Friend" - After getting attacked by the insane Shadow Woman in the Floating Red Tiles world
#73 - "Twintails Maid" - When using the Twintails effect with the maid outfit in the Dressing Room
#74 - "Turn of the Month" - When you use the Glasses effect during the Lonley Urotsuki event*
#75 - "Glasses Suit" - When using the Glasses effect with the suit in the Dressing Room
#76 - “Do Not Disturb” - After getting the Wolf effect
#77 - “Sun & Woman” - After trying to chainsaw the lady under the big red sun in the Pastel Blue House
#78 - "Mushroom" - After you first enter Mushroom World
#79 - “Hanging Child” - When coming across the Koshukei-tan near the laggy map
#80 - “Detour Around My Face” - After walking near your ghost in Atlantis
#81 - "Monster" - After eating the cheese that turns you giant in Toy World and crushing a certain amount of buildings in Mini-Town
#82 - "Watering" - After talking to the Farmer in Farm World
#83 - "Howling At The Moon" - When using the Wolf effect to howl at the moon on the nighttime in Day & Night Towers
#84 - "Not & Marginal" - After reading the first book on Urotsuki's left on the first bookcase in the Library
#85 - "Do You Also" - After interacting with Oni Musume while she's reading
#86 - "★Penguin★" - After getting the Penguin effect
#87 - "My World" - When you first enter any of the dream worlds in the Nexus
#88 - "Director" - After sitting in the chair next to Yume in Tapir-San's Place
#89 - "bonsoir, mon r" - Random occurrence
#90 - "Dreams・Dreams・Dreams" - After getting the Child effect
#91 - "B-Kun Excretion Festival" - After using the Boy effect in the Bathroom in the Dark Room
#92 - "Box Child" - When finding Hakoko in the box in the Eyeball Shop
#93 - "Dokokano Night B" - After laying in Urotsuki's bed in the dreamworld.
#94 - "TP Child Alone" - When you use the child effect before viewing the Lonely Urotsuki event at the Underwater Amusement Park
#95 - "Why? BOKN Cliff" - When you chainsaw the girl at the Outlook in the Invisible Maze
#96 - "They're Scraped" - When you look at the fifth book from Urotsuki's right on the first bookcase in the Library
#97 - "20" - Interact with everything on this wallpaper*
#98 - "Me Without Color" - Random occurrence
#99 - "Maiko" - After getting the Maiko effect
#100 - "Full Smail!" - After visiting Smile-san and making him laugh
#101 - "Crying/Laughing" - After chainsawing the crying white creature in Blood World
#102 - "Hat" - After meeting the lady underneath the big red sun in the Pastel Blue House
#103 - "Drunk" - When you buy one or more drinks at the Underground Bar
#104 - "Where You Are Staring" - When encountering a sane Shadow Woman
#105 - "Fall" - After falling down from completing the Penguin GB Game in Urotsuki's Dream Apartments
#106 - "Red Book" - After first interacting with Oni Musume
#107 - "Submerged Underwater" - When using the Glasses effect near the puppet theatre on the Ocean Floor
#108 - "Chainsaw" - After getting the Chainsaw effect
#109 - "Circus Tent" - After finding the albino girl in the tent at the Circus and escaping without the clown trapping you
#110 - "Plaster Cast" - After getting the Cripple effect
#111 - "Sink" - When you first go to the Ocean Floor via the submarine
#112 - "How It Is In My Room" - After encountering the long-haired girl in Urotsuki's Dream Apartments
#113 - "dream" - Random occurrence
#114 - "! TP Human Sacrifice" - After Urotsuki gets crushed on one of the pillars at the Underwater Amusement Park
#115 - "I Will Not Come Back, Box Child" - When using the Bug or Fairy effect to make Hakoko pop her head out
#116 - "Urotsuki" - When you have 22 effects (counting the Instructions)
#117 - "Without Zero" - When encountering the XY twins in the Apartments
#118 - "Bonk!" - After getting the Child effect
#119 - "You Can't, Red" - After getting the Red Riding Hood effect
#120 - "Devas' Confinement" - After getting caught by all the shadow chasers on this wallpaper
#121 - "Black Witch Invisibility" - After using the Invisible effect on the sane Shadow Woman found in front of the tic-tac-toe board in Toy World
#122 - "Two Submarine People" - When encountering the Commando and Provost-san
#123 - "Whoa! Dazzling" - When you first enter the room with the silhouette on the ground in the Pastel Blue House
#124 - "Papa T" - When you interact with the Blue NPC in the Arrow Maze
#125 - When you first enter the Broken Faces Area
#126 - "Tissue" - After getting the Tissue effect
#127 - "Red Love" - When you get 24 effects (counting the Instructions)
#128 - "Amentia" - When you first enter Bane Jack's room where the Spring effect is found
#129 - "Urotsuki With Blood" - After Urotsuki gets crushed on one of the pillars at the Underwater Amusement Park
#130 - "Tatami Room Loneliness"" When you first visit the giant bedroom from Toy World or the Gray Road
#131 - "A Chainsaw" - After getting the Chainsaw effect
#132 - "In the Water Tank" - After visiting the Power Plant and falling into one of the tanks
#133 - "Residents of the Dream World" - After meeting all the characters on this wallpaper
#134 - "Amusement Park Loneliness" - After viewing the Lonely Urotsuki event in the Underwater Amusement park
#135 - "Little Red Riding Hood" - After getting the Red Riding Hood effect
#136 - "Prince & Princess" - After encountering the prince and princess cutouts in Theatre World
#137 - "Shrine" - When you first enter the Shinto Shrine
#138 - "Bathhouse Scene" - When you first enter the Hot Springs
#139 - "Everyone's Dream" - After getting the 1st Ending
#140 - "Dolphin Puzzle" - After unlocking all the Kura Puzzles
#141 - "Flesh & Blood Babies" - When you first enter the Closet Pinwheel Path
#142 - After playing for 30 minutes (not including time the menu is open)
#143 - "Fiction & Reality" - After seeing the monochrome boy change to red on the Sakura Path in the Shinto Shrine
#144 - "I Dreamed of the Universe." - When you first enter Flying Fish World
#145 - "Sneering Shadow img" - When you use the Telephone effect on Smile-San in Flying Fish World
#146 - "Rainbow Bridge" - When you use the Teru Teru Bōzu and Rainbow effects to make a bridge at the Tribe Settlement
#147 - "Those Who Lurk Underground" - When you first go to the Underground TV Complex
#148 - "Soldier" - When you go to the room with the army NPCs in the FC Basement
#149 - "Momentary Break" - After you change into the swimsuit at the hotel in Japan Town
#150 - "Starting the Pulse" - When you use the lantern effect in Heart World
#151 - "DimensionWorld"
#152 - "Haniwa" - After you view the Haniwa Dance event at the Haniwa Temple
#153 - "Egg"
#154 - "What Do You See?" - When you interact with the mirror behind the wizard in Jigsaw Puzzle World using the marginal effect and change into a witch
#155
As for #74 and #97, note that these wallpapers are known to be very tricky to get. You may need meet the requirements multiple times before you obtain it or may need to do something entirely different (i.e. crying with the Stretch effect at the Lonley Urotsuki event for #74, interacting with a specific 'TV NPC' at the Underwater Amusement Park for #97).