The problem with this thread is that there's a big gulf between a game that's replayable and a game that's what you would consider a damn good game. On top of this there are games which are not really replayable and are also not very good games but are just very, very long games, so it feels like it's worked its way into your heart. There are also games which fill one with nostalgia but not a lot else, a sort of time induced fanboyism for stuff that's probably shitter than you think it is. Then, when it comes to writing out a list you have to wonder what the reader is going to get out of your list, do I write for the audience or do I write for myself, the former requiring the answers to be of actual use to the reader and the latter just being an exercise in memory recall and self flagellation.
So what I've decided to do is just do a quick advert for a bunch of games I think certain other (prestigious) people here might like but possibly haven't played yet. They aren't my definitive top 10 of all time, but they might be and it probably wont be 10 either:
Icewind Dale 1 - Vanilla only. Not the very first vanilla but the one that was the result of the first post-release patch, still pre-Heart of Winter. Playing with the Heart of Winter expansion installed changes the game radically, across the board, so if you've never played vanilla IWD then it could well feel like a completely different game. If you happen upon the very rare original vanilla, beware, it was quickly patched for a reason and you'll be able to tell if it's original vanilla because +2 weapons can't hit the Snake Queen.
It's a RTwP cRPG using the AD&D ruleset with a focus on combat and hack'n'slashing but with plenty of other nice surprises of all types along the way.
Medieval: Total War - Again, vanilla is fine but with this game I'd recommend installing it with the Viking Invasion expansion pack, but just not bother playing the Viking Invasion part as the main game gets the very useful upgrade of allowing you to arrange your troops before battle if you do, something that's quite annoying on pure vanilla (but still manageable).
It's a 4x game where you manage your empire and build improvements on a huge map but then zoom to actual battlefields to fight big battles in Real Time with 100s to 1000s of troops, all of which are commandable by you.
Myth: The Fallen Lords - I think there's only one version of this around, though I could be wrong.
It's a Real Time Squad Tactics game where each mission forms a chapter in a wonderfully narrated greater quest. It was an early 3D polygon graphics game, so the backgrounds are pretty hilarious by today's standards but the units themselves are none too unattractive eye catching sprites. Friendly fire is not turn offable.
Robin Hood The Legend of Sherwood - Again, no idea about versions.
It's another Real Time Squad Tactics game where each mission forms a story in a greater narrative, the difference with this game being there's a whole lot more to fathom out with regards to getting your posse to behave at the optimum and maintaining a large force, not to mention combining both murderous and non-murderous solutions. Requires a sense of humour as it's more light hearted than the one above, if no less challenging. A very polished game in practically every respect.
Any Worms game from 1995-2002 - version immaterial.
Another Squad Tactics game but this one is turn based and there is no grand narrative though they do have campaigns but they are not linked narratively. Also requires a sense of humour and, again, friendly fire is not turn offable.
Civilisation III - Complete Edition (otherwise known as Conquests) which improves the game greatly from both Vanilla and then the Play the World expansion by allowing such cool things as, amongst others, Armies and Small Wonders.
It's a Turn Based 4x game and is considered 'The Middle Child' of the Civ series as it still adheres to many of the visuals and rules of the first two in the series but is the first to start experimenting with a greater focus on peaceful victories, particularly with it's Culture mechanic. There are so many variables in this game that even to this day the top players still argue about the 'best' way to achieve xyz destination and what is the 'best' way to play.
Grand Ages: Rome - Gold Edition including the Augusta expansion, because the vanilla seems so lacking after the highly worthwhile additions from the upgrade, though I've yet to play Augusta itself yet, again, it's mainly for the improvements to the main game.
It's a Real Time Strategy Building game with the added bonus of mini Total War-like Real Time combat on many of the 36 individual missions which all form a coherent/historically accurate narrative of the period from pre-Julius Caesar to Octavius, including Cleopatra, Pompey, Marc Anthony and the like. There are actually 40 missions in all but on two occasions you have to choose which mission path to follow, the first of which could leave you with quite a few less missions. You play a non-active leader who levels up and buy's bonuses with rewards. There is no friendly fire but if you're not careful your buildings will catch on fire, most probably while your citizens die from the plaque during an earthquake.
Streets of Rage - Arcade version, though I've no idea if there's even any differences in versions. Not to be confused with Street Fighter games.
It's a Side Scrolling Beat'em Up which, for me, is the original and best, though I'm aware many people hold Golden Axe in this spot. You punch, slash and bash your way through the mean streets, what more do you need to know. It's double the fun co-op for two player mayhem. You cannot turn off friendly fire.
Age of Wonders: Shadow Magic - The 3rd game in the series even though it's not Age of Wonders 3, just another classic game-numbering balls-up. Like Homm 3, there's just that something special about this one that tips it from niche-specialist into an everyone-should-play-it.
It's a 4x Turn Based Strategy game in a fantasy environment which unfolds in either missions on a campaign or one-off scenarios. It's one of those games that's not easy until you get the hang of it and then still manages to provide a challenge while also managing to be immensely fun and varied, with such golden highlights as levelling up very squishy baby dragons into big adult scary dragons.
Max Damage - No, not that one, the flash game, and the original one at that.
It's a classic 50 level Physics flash game. Of all the flash games I've played, none have caught my interest like Max Damage. Some levels will have you tearing your hair out, other will be incredibly easy and some just right, but whichever, there's just something about it that's so... perfect. Max fires various projectiles from a toy cannon in the hope of damaging valuable household items. And, yes, beginning to tire now, so gonna stop and this makes 10 so...
I would say the least perfect game (IMO) on this list is probably Civ 3 but that's the one I've put the most hours in and play most regularly.