Mmm, dad relationships. Well, my father and I share one HUGE common interest: pc games! He pretty much raised me in front of a computer, as soon as I could sit up. And the one game we loved playing together above all others (or well, I point out monsters and items and traps and things, and he shoots stuff) was Return to Castle Wolvenstein. We still maintain a tradition of playing through it once a year, even now that it's massively outdated. And somehow we began to play together in the same way every new Call of Duty game he gets, so that's a thing, too.
Other than that he has a ridiculous sense of humour. As in, the term "Dad jokes" was made for him. Usually I don't mind them (actually, used to love them most of my life - I've got a similar sense of humour), but they've become more irritating lately. That's probably me, not him.
Other than games we've got some other common interests, too. He's a typical professor type and a gaming addict (some 1st person shooters, lately Skyrim too, but mostly strategy games like Sid Meier's Civilization, Tropico, ANNO, etc. He's usually somewhere in the top level of Tropico's online lists). Odd combination, but it works. So anyway, we're both really interested in history, theology, political developments (more as in why people do the things they do as to what they actually do), and stuff like that. Languages, too, though I'm more interested in that than he is, and sometimes I can have better talks with my mother about the topic (she was incredibly interested in linguistics in uni).
So... I have a pretty good relationship with my father. A little more strained the more I grow, but good all the same. Most trouble comes from me getting irritated with him, rather than the other way round.