On the surface, no: we have quite different political views and in a sense that's the most obvious difference, since both of us are quite passionate about it and both seriously considered going into it professionally before we got together (thank goodness we didn't - would have lead to some tricky situations!)
In terms of musical tastes, I am far from "down with the kids" and my CD collection is firmly stuck in the 80s, but H looked up from the BBC website when Michael Jackson died and asked me who he was - no connection with any popular culture.
TV we don't really watch, although we do both enjoy shows set in the world of UK politics like Yes Minister (see above!) I have slowly and quite successfully been introducing H to the world of films, working our way through the Best Picture Oscar winners since the 1970s, although I fear he will never share my passion for John Hughes films.
In terms of what we like to do in our spare time, the main things for both of us are travel and reading, and luckily we share similar tastes there. We're also in the same profession so similar lifestyles. We also share the same faith (although we have quite different theological views) - I don't think that's so important but in practical terms it makes things easier. I think we share some fundamental moral and philosophical views about equality etc. despite our political differences. It's the latter stuff that's more important really.