I realise this thread belongs in the classic games forum, but cherynobyl has more visitors than that place :D
Ok, I'll go first, in NO particular order :
1) Mooncresta (ZX Spectrum) - Galaxian style 2D shoot em up, introduced me to the fast paced world of shoot em ups, a genre that seems to have died. Dodging alien ships and millions of round bullets while trying to annihilate your enemies. Very simple in every way, but playable to the extreme - evidence that graphics and sound do not make a game.
2) Flashback (Amiga/Megadrive/SNES) - 2D action/adventure/platformer featuring a superb plot, realistic game physics, a ton of missions to complete, fluid graphics, and truckloads of atmosphere. From the developers of the classic 'Another World', which was also way ahead of its time. Flashback was sequelled but the next in the series was at best unremarkable. Another genre that seems to be all but dead.
3) Syndicate (Amiga,PC) - Gave birth to the term 'squad based shooter'. Take your group of 4 cyborg mercenaries on increasingly dangerous missions in the violent futuristic blade-runner-esque underworld. Gun down gang members, enemy cyborgs, cops or just innocent people, depending on what sort of commander you are. Was succeeded by syndicate wars, which I haven't actually played yet.
4) Monkey Island 1 + 2 (Amiga,PC) - Introduced me to the point and click genre, and stirs many fond memories of 3 headed monkeys and other craziness. Some may argue that these games were boring, but they really made you use your head - you'd find yourself thinking up solutions while eating lunch, watching telly or whatever. Several other point and clicks of note are Day of the Tentacle, and the Indiana Jones series. Neither beat the monkey island games though.
5) Super Mario World (SNES) - My favourite Mario game of all time. 96 levels in all if I remember correctly. This came as close to perfection as any game could get in my opinion, and singlehandedly converted me to a nintendo fan virtually over night.
6) Zelda : A Link to the Past (SNES) - First RPG I played. Brilliant storyline, great japanese style cartoony graphics. Hundreds of locations to visit. Atmosphere to the max. Great.
7) DOOM Series (PC) - Easily the games I have spent most time playing, be it on the single player campaigns, Multiplayer LAN/Modem or creating new levels for it. Way ahead of its time, atmospheric, incredibly well designed and was the first game to make me realise PC's were not just for people working in offices. Superb.
8) Command & Conquer + Red Alert Series (PC) - Introduced me to the RTS genre, and still in my opinion the best of their type. The red alert games were slightly better than the C&C ones in my opinion, as the weaponry and storylines were more plausible and closer to modern day events. The balance between all the structures and units in the games is nothing short of remarkable. Multiplayer is a nasty tactic creating dream.
9) Goldeneye/Perfect Dark (N64) - The surprise hit of the decade, goldeneye shot to classic status instantly, and still holds its own against other shooters of today in my opinion. Perfect Dark, though containing a weaker single player campaign, took multiplayer to new levels, and with all those excellent weapons, arenas, characters and options, you could create just about any game of your liking.
10) Grand Theft Auto 3/Vice City (PS2, PC, XBOX) - Jumped from fun 2D killfest to the creation of a multigenre shooter/driver which allowed an unprecedented amount of freedom. Feel what it is like to be a mafia gangster with little or no morals and a bag full of guns.
Quite a lot there, I must be bored :D
If you are thinking about games like Sonic Gems and Sonic Mega collections, then they aren't new games. Also, Sonic Adventure 1 and 2 were originally on the Dreamcast so still not new. They were all playable anyway so I don't see where the 'rubbish' comment comes in...