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 146 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 - After sleeping 3 times
#4 - When you first enter the Hand Hub
#5 - When you activate the Buddha Rave event in Marijuana Goddess World
#6 - After collecting 5 effects (including the instructions)
#7 - When you interact with the painting of the same image in the Art Gallery
#8 - When you interact with the painting of the same image in the Art Gallery
#9 - After looking at the fourth book from Urotsuki's left on the second bookcase in the Library
#10 - After getting the Fairy effect
#11 - Random occurrence
#12 - After going to the "Green Monster Party" in Garden World
#13 - When you first enter Theatre World
#14 - When you first enter Japan Town
#15 - After getting the Rainbow effect
#16 - After sleeping 10 times
#17 - When you first enter the Underground Bar
#18 - When you use the Rainbow effect at the Snowy Pipe Organ
#19 - When you first enter room with the purple wavy lines on the floor at the Underwater Amusement Park
#20 - When triggering Odorika's full screen dance event
#21 - Random occurrence
#22 - When encountering the Commando and Provost-san when the submarine is not open
#23 - After encountering Mother in the Urotsuki's Dream Apartments
#24 - When you interact with the giant mannequin in Nail World
#25 - When you first enter Sign World
#26 - After chainsawing Tapir-San's back to get into Space
#27 - After getting the Glasses effect
#28 - After using the Fairy effect on Tako Otoko
#29 - After entering the first painting you see in the Art Gallery after going through the easel
#30 - When you first enter Atlantis from the grand piano at the Snowy Pipe Organ
#31 - When you swim down the road leading to the Underwater Amusement Park
#32 - After interacting with Cripple-tan
#33 - After getting the Boy effect
#34 - Random occurrence
#35 - After getting the School Boy effect
#36 - After getting the Spring effect
#37 - When you enter Urotsuki's Dream Apartments and turn on the TV
#38 - After entering Valentine Land from Sign World
#39 - When you first enter Chocolate World
#40 - After chainsawing the sane Shadow Woman in Forest World, going underground and then emerging
#41 - When using the glasses effect on the nighttime ledge Day & Night Towers
#42 - When you interact with the Music Box Woman found in Nail World
#43 - When using the Telephone effect on the Oni Musume while she is reading
#44 - When you interact with the painting of the same image in the Art Gallery
#45 - When you first enter Sand Desert Land
#46 - When you first enter the clown's dungeon in the Underwater Amusement Park
#47 - After interacting with the Boy on the Bench in the Blue Forest
#48 - After interacting with the Beret Twins
#49 - When you first enter Teddy Bear Land
#50 - After interacting with Megusuri Uri in the Eyeball Shop
#51 - After trying on the winter gear in the Dressing Room (You must have completed the Snow Gunikki minigame)
#52 - After using the Cake effect on Sweets Musume
#53 - After meeting Elvis Masada
#54 - After getting the Cake effect
#55 - Random occurrence
#56 - After completing the ↑V↑ minigame
#57 - After coming across the creatures in tanks at the Power Plant
#58 - When you first enter Monochrome Street
#59 - When encountering Dogboa
#60 - After getting abducted from the Apartments
#61 - When encountering Yukata
#62 - After interacting with the Blue Crying Man after the Zalgo event
#63 - After getting the Twintails effect
#64 - When using the Telephone effect on Oni Musume while she is reading
#65 - After using the Cake effect on Sweets Musume
#66 - When you climb up the ladder to Tapir-San's Place
#67 - After viewing the lonely Urotsuki event in the Underwater Amusement Park
#68 - After sleeping 30 times
#69 - After activating the cloning machine in Toy World
#70 - After chainsawing your "reflection" in a room in Day & Night Towers
#71 - When communicating with the grey NPCs in Marijuana Goddess World
#72 - After getting attacked by the insane Shadow Woman in the Floating Red Tiles world
#73 - When using the Twintails effect with the maid outfit in the Dressing Room
#74 - When you use the Glasses effect during the Lonley Urotsuki event*
#75 - When using the Glasses effect with the suit in the Dressing Room
#76 - After getting the Wolf effect
#77 - After trying to chainsaw the lady under the big red sun in the Pastel Blue House
#78 - After you first enter Mushroom World
#79 - When coming across the Koshukei-tan near the laggy map
#80 - After walking near your ghost in Atlantis
#81 - After eating the cheese that turns you giant in Toy World and crushing a certain amount of buildings in Mini-Town
#82 - After talking to the Farmer in Farm World
#83 - When using the Wolf effect to howl at the moon on the nighttime in Day & Night Towers
#84 - After reading the first book on Urotsuki's left on the first bookcase in the Library
#85 - After interacting with Oni Musume while she's reading
#86 - After getting the Penguin effect
#87 - When you first enter any of the dream worlds in the Nexus
#88 - After sitting in the chair next to Yume in Tapir-San's Place
#89 - Random occurrence
#90 - After getting the Child effect
#91 - After using the Boy effect in the Bathroom in the Dark Room
#92 - When finding Hakoko in the box in the Eyeball Shop
#93 - After laying in Urotsuki's bed in the dreamworld.
#94 - When you use the child effect before viewing the Lonely Urotsuki event at the Underwater Amusement Park
#95 - When you chainsaw the girl at the Outlook in the Invisible Maze
#96 - When you look at the fifth book from Urotsuki's right on the first bookcase in the Library
#97 - Interact with everything on this wallpaper*
#98 - Random occurrence
#99 - After getting the Maiko effect
#100 - After visiting Smile-san and making him laugh
#101 - After chainsawing the crying white creature in Blood World
#102 - After meeting the lady underneath the big red sun in the Pastel Blue House
#103 - When you buy one or more drinks at the Underground Bar
#104 - When encountering a sane Shadow Woman
#105 - After falling down from completing the Penguin GB Game in Urotsuki's Dream Apartments.
#106 - After first interacting with the Oni Musume
#107 - When using the Glasses effect near the puppet theatre on the Ocean Floor
#108 - After getting the Chainsaw effect
#109 - After finding the albino girl in the tent at the Circus and escaping without the clown trapping you
#110 - After getting the Cripple effect
#111 - When you first go to the Ocean Floor via the submarine
#112 - After encountering the long-haired girl in Urotsuki's Dream Apartments
#113 - Random occurrence
#114 - After Urotsuki gets crushed on one of the pillars at the Underwater Amusement Park
#115 - When using the Bug or Fairy effect to make Hakoko pop her head out
#116 - Random occurrence
#117 - When encountering the XY twins in the Apartments
#118 - After getting the Child effect
#119 - After getting the Red Riding Hood effect
#120 - After encountering all the shadow chasers
#121 - After using the Invisible effect on the sane Shadow Woman found in front of the tic-tac-toe board in Toy World
#122 - When encountering the Commando and Provost-san
#123 - When you first enter the room with the silhouette on the ground in the Pastel Blue House
#124 - When you first enter the Arrow Maze
#125 - When you first enter the Broken Faces Area
#126 - After getting the Tissue effect
#127 - Random occurrence
#128 - When you first enter Bane Jack's room where the Spring effect is found
#129 - After Urotsuki gets crushed on one of the pillars at the Underwater Amusement Park
#130 When you first visit the giant bedroom from Toy World or the Gray Road
#131 - After getting the Chainsaw effect
#132 - After visiting the Power Plant and falling into one of the tanks
#133 - After meeting all the characters on this wallpaper
#134 - After viewing the Lonely Urotsuki event in the Underwater Amusement park
#135 - After getting the Red Riding Hood effect
#136 - After encountering the prince and princess cutouts in Theatre World
#137 - When you first enter the Shinto Shrine
#138 - When you first enter the Hot Springs
#139 - After getting the 1st Ending
#140 - After unlocking all the Kura Puzzles
#141 - When first entering the Closet Pinwheel Path
#142
#143 - After seeing the monochrome boy change to red on the Sakura Path in the Shinto Shrine
#144 - When you first enter Flying Fish World
#145 - When you use the Telephone effect on Smile-San in Flying Fish World
#146 - When you use the Teru Teru Bōzu and Rainbow effects to make a bridge at the Tribe Settlement
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).