At universal the ride i've heard the most issues with when it comes to height is Dudley Doright's log flume ride because of the design of the lap-bar. I've never ridden it so I can't speak from experience sadly.
Beyond that, I'm 6'6" and at Universal I've never really had an issue fitting on any rides, and I'm assuming my legs and upper body are probably going to be longer than yours. Sometimes for lap-bars I'll have to resort to the ole "cross your ankles" trick, but there hasn't been anything that's been a real issue.
At Disney things are a bit more complicated. Boat rides like Small World and Pirates require sitting sideways to fit my legs, and Space Mountain is painful because of the T-Bar and how wide my legs have to be spread to get it down to my lap. (But again, at 6'2" i don't think you'll have that problem)