Hmm, that's a tall order to only pick one game series that deserves a reboot. Especially since some of the games that I've loved over the years come from different genres.
So, I think I'll have to list a couple:
-- Flight Simulator genre: X-Wing series. Yes, I'm a major fan of Star Wars (still remember seeing ANH at the drive-in as a kid). But while there are a number of flight-sim games I've played & loved over the years (like the old Chuck Yeager DOS game, or even Microsoft's Combat Flight Simulator 1 & 2), the reason I love flight-sim games is because of (IMHO) the flight-sim series: X-Wing, TIE Fighter, X-Wing vs. TIE Fighter, & even X-Wing: Alliance. Dogfighting with classic Star Wars fighters, making torpedo runs on Star Destroyers, what's not to love? And with the new films already out & on their way, it's the perfect time to reboot the game franchise.
-- First-Person Shooter: SWAT series. Again, I'm a long-time FPS player. Starting back in the Dark Ages with Castle Wolfenstein 3D, Doom/Doom 2, Heretic, & even the early Quake games, I've continued it up to more modern times (Halo: CE is still a go-to online game for me whenever I have an hour or so, & I really enjoy playing BF4). But SWAT is just something else. Like with the Battlefield series & other "realistic" FPS games, you're going to die quickly if you simply try to "run and gun" against the opposition. And the different multiplayer game modes are so different from other FPS games (like VIP escort, one of my favorites but also the source of much angst when it comes to actual play). But the biggest reason I loved it (& why my brother-in-law & I used to spend so much time playing SWAT 3 & SWAT 4 over our LAN)? Arresting the opposing team. Very few games have an option that lets you neutralize the opponent without shooting them...let alone one that gives you more points (standard points on multiplayer were 1 point per kill but 5 points per arrest). And let's not forget how your loadout & tactical gear not only had pros & cons (like how the gas mask meant you were immune to pepper spray, CS gas & pepper-loaded paintball guns, but meant you were blinded by flashbangs), but it had a noticeable effect in game (i.e. heavy armor let you shrug off "sting" grenades much more quickly, but meant you moved slower & took longer to arrest somebody).
Fortunately for me, they've already 'rebooted' my favorite RTS (StarCraft II), or I'd have to add that one as well.