Besides any game with a silent protagonist?
Most RPGs. Pretty much every Final Fantasy game. Kain, Edgar, Red XIII, Quistis, Vivi, Auron, Basch, Sazh as opposed to whoever the protagonist was. I liked Zelos over Lloyd in Tales of Symphonia, Raven (slightly) more than Yuri in Tales of Vesperia (though in terms of protagonists, Yuri is one of my favorites).
I prefered Zero to Megaman X, but apparently most people did because he got revived, promoted to deutertagonist, and then shared the main character spotlight... and then he got his own series.
Alucard over whatever Belmont (or Soma) is in that Castlevania.
The issue I guess with main characters is that you're much more likely to get angsting and dramatics from them, because they are the centerpiece of the story. The side characters won't act as melodramatic just by virtue of having less focus.
Also a ton of them follow the "JUSTICE HEROOOO" archetype, which is annoying to me because they not only have an infallible sense of justice and righteousness, but the means to carry it out and change the world. If they're not that, then there's a chance they swing too far in the other direction and try to be an anti-hero, and that can make them feel like they're trying too hard to be edgy.
Honestly, if I do like main characters most it's because they're believable and realistic, or because the rest of the cast is absolutely dull or unlikable.