I do love a lot of old games still, and with certain series I don't just play the one, I have a tendency to do a complete playthrough of all of them. Resident Evil, notably, and I try to keep to chronological order as best I can. I start with Zero, then play all forms of the first game (REmake, now in lovely HD, the old PS1 original, the DS version, and Directors Cut), 2, 3, Code Veronica X, 4 and 5. I own but have never played 6, oddly enough. Sometimes I include the Gun Survivor side-series, was never really keen on the Outbreak games, I still have Gaiden but don't fancy rooting around for an old GameBoy to play it, and I may also play Umbrella and Darkside chronicles too. Out of all of them, Resident Evil 2, 3 and 4 have been my most played games of the entire series, my brothers and I over the years since we got them when they were released must have completed them about 1,000 times, which may not even be an exaggeration.
Legend of Zelda: A Link to the Past, Ocarina of Time and Twilight Princess. Although I have OoT on 3DS and as a bonus disc that came with my Gamecube copy of WindWaker (I play the HD version of this one a lot on Wii U), I still prefer to dig out the N64 and play my original copy which I may have alone completed it near enough the same amount of times as the RE games :D
Metal Gear Solid. I still like this game a lot and much prefer the PS1 version to Twin Snakes.
Fable 2. It still brings me joy, though I was annoyed when I only recently found out that you can have the Highwayman's coat open OR closed at the simple tap of the A button when viewing it in the menu, as I always complained whenever you encountered the Highwaymen in the game that they got to have theirs closed and it looked so cool. I'm such a pillock! :D
Kingdom Hearts 1 and 2. Still loving the new HD editions :D
Halo trilogy. My brother and I play co-op Legendary mode on all but the 2nd, which had that irritating 'one dies/start all over again' system which was especially annoying once you got caught out by a damn sniper. The first game we must have completed well over 100 times, and is still fun to play when you just want to run in and blast the flip out of something.
Black. I enjoy it so much that I play through on Easy, Normal, Hard and then Black Ops modes. It's also a way to play for as long as possible with regular weapons before they turn silver and have infinite ammo without deleting the profile over and over.
Final Fantasy 8 and 9. 9 was the first FF game I played, and the one I have completed the most, I still cannot get enough of it and play it on PSP. 8 is my second favourite, and have completed that one lots and lots too, and again still play it on PSP.
Prince of Persia: Sands of Time and Two Thrones. They're still enjoyable, I especially like the Two Thrones stealth-kill mechanics, it made the game a lot more enjoyable after the irritatingly combat-heavy Warrior Within which I did like back in the day, but have grown tired of now. The other two I still enjoy, and also like the Prince of Persia game on Xbox360/PS3 which other people didn't seem to like.
Jet Set Radio Future. I may love this game until the end of time!
Sam and Max Hit the Road. Now this is an oldie, and I still love it for the humour ^_^
TimeSplitters 2 and Future Perfect. I really wish they made more L
Games I used to play a lot but haven't tried them again in years include Tales of Symphonia, Devil May Cry, Silent Hill 1-3, Dino Crisis 2 (I watched Jurassic World and I actually want to play this again now :D ), Star Wars Knights of the Old Republic, Star Wars Jedi Power Battles (This I will definitely never ever play again, it was awful even back in the old days but it was one of the few co-op games around for my brothers and I), WWF: SmackDown! and SmackDown! 2: Know Your Role, Medal of Honour: Frontline (with perhaps one of my all-time favourite videogame soundtracks), Tekken 3, Pokemon Blue and Pokemon Sapphire.