This is a bit like the last one, where a lot of games instantly rule themselves out because they are specifically designed as one-shots, or for very short story arcs, but for the rest of the RPGs out there it's more a case of who your players are, and who your GM is.
I like the idea of a game with a distinct beginning, middle and end. But I know a lot of people who are always striving for that epic game that lasts for years and years. 5 to 10 games is probably a nice length for a short to medium campaign, and I'd even consider something like D&D for it. I wouldn't start at level 1 though, I'd probably run a game where the players started at about level 4 or 5, and over the course of the game I'd allow the characters to gain 2 or 3 levels. I always found the sweet spot for 3rd Edition D&D to be around level 5 or 6, so this means our characters start at the point where the game gets a bit meatier, but the game also ends before the characters become too overpowered compared to the world around them.
If were going to run another system, I'd have to seriously consider the type of progression that occurs over a period of ten sessions. Early Warhammer Fantasy would probably be another contender, but it's a dark gritty setting... every time I've played it, we've been lucky to see characters progress through a career more than once every two or three games, and a lot of those low level careers are pretty brutal. A ten session arc in this system, starting at base level would be lethal to many of the characters, but if that's what you were going for than I could see it working.
This is actually one of those games that I'd like to have experimented with a bit more. Perhaps trying to run a game where players have a certain amount of XP under their belts, and a few career paths that they'd already traversed to become veterans. But it's always been a slog to get the that level when everyone decides that we need to start the stories with all the characters at base level. A mid level campaign of this would definitely work over a 10 session arc.
I generally think most of the long-form, campaign-oriented RPGs would work well with the 10 session game format.