Although I've collected brief experiences with most of the computers Tezza listed in his first message, I'll stick with those I know by heart.
Amiga 500
Business/work: Hmm.. Deluxe Paint, SoundTracker.. perhaps OctaMED which follows the same principles as SoundTracker but greatly improved and with its own formats. Its ancestors are still developed for Windows PCs today.
Game: There are so many to choose from. Personally I like the Pinball Dreams and Pinball Fantasies games by Digital Illusions. Partly because the 386 conversion of Pinball Dreams was truly terrible, to the point people claimed a 7 MHz Amiga 500 was vastly superior to a 33 MHz 386. Of course this is BS, which was shown by the nice PC conversion of Fantasies.
Utility: Ditto. The whole Workbench in some respects was refreshing even compared to MS Windows. But if I should pick one utility, I'd go with Directory Opus, another program I believe still exists today in Windows versions. It is a file explorer loaded with configurable buttons which lets you view, play, unzip, move, encrypt etc files as you select them.
Commodore VIC-20
Business/work: Not so many memorable applications in that sector. There were a bunch of word processors, but word processing on a computer that can display 20-25 characters per row is not so much fun, even though the keyboard is rather good. Perhaps I'll name a Basic expansion although they probably belong under Utilities. In order to not draw a blank, I'll throw in Super Expander +3K in this category. Programmer's Aid, HES Mon and a few others might qualify too.
Game: Most VIC-20 games were arcade ports or from other systems. Games such as Omega Race, Jelly Monsters, Jupiter Lander, Gorf, Shamus and so on hold good quality, but are not unique to the VIC or arguably the best versions. Tom Griner wrote a couple of remarkable games, and so did Jeff Minter too. Perhaps I'd select something from Minter's production: Gridrunner, Laser Zone or Matrix. If I remember correctly, one of those is known as Attack of the Mutant Camels in the USA, not to be mixed up by Jeff Minter's C64 game with the same name.
Utility: Hrm, same story as with the business software. I'll play safe and throw in the DOS Wedge found on the 1540/1541 Test/Demo disk. It adds the > for sending commands to the disk drive, $ to view the directory and I think even shortkeys to load and save programs. No turbo though, but sometimes quite handy to load.
Commodore 64
Business/work: Hm, probably the GEOS suite, which is a whole operating system rather than a single piece of software. I'd also like to nominate Calc Result Easy/Advanced by Handic Software, which is less known but once upon a time a relative smash hit, ported to the IBM PC and released directly after Lotus 1-2-3 had entered the market.. and that was the end of Calc Result.
Game: Everyone have their personal favorite: arcade conversions, games from other formats.. Since you asked for nominations that boggle your mind, thinking "this is not possible", I'll recommend one of the last commercial games for the C64: Mayhem in Monsterland from 1993. It is a bit of a Sonic rip-off, but technically very advanced. You think the C64 has been upgraded (?) to at least a NES, perhaps even a 16-bit video game.
Utility: Ah.. time for more cartridges. There was a "religious war" between the Final Cartridge 3 crowd and those who preferred Action Replay V - VI. Both are fine pieces of C64 history, and essential for anyone who wants to cheat in a game, get a cheap, instant disk turbo, machine code monitor and more. The Final Cartridge was said to be more targetted towards gamers with boxes full of tapes in Turbo Tape format, while Action Replay perhaps aimed a bit more at developers and productive people. I've been a proud Action Replay owner since .. 1990 or so. Nowadays, the heritage from these freezer cartridges remain in form of Retro Replay and latest MMC Replay.
Now, I'm done with this message. :-D