Not that many, but a lot. I'm halfway through NG++ now with 239 total deaths. Maybe 80-100? I'm also using a gold maximizing style, not a death reducing one. Once I max out my upgrades I'll start locking the castle and having a lot less deaths.
Because Rogue Legacy isn't a AAA title, it doesn't get the kind of attention Dark Souls does for being a "hard game", even though it makes Dark Souls look like child's play in degree of difficulty. In comparison, I died 15 times with my sorceror character in Dark Souls, only my second character in the game.
If anyone thinks Rogue Legacy is too easy for them, try another great game, I Wanna Be the Guy: Gaiden.