I’m going to answer this going on what would be thematically interesting, since in my opinion the best possible type combinations from a strategic perspective exist already (Dragon/Fire offensively and Steel/Psychic with Levitate defensively).
I have many favourites. I think the one I’m most hoping for is Water/Fire, just because I think there are a lot of clever things that could be done with it. The combination of elements is interesting, because normally we’re used to thinking of their relationship as “water douses fire,” but then again, combining water and fire gives you steam, something new and powerful.
Normal/Ghost would be interesting for something that, thematically, exists between life and death, maybe stressing the idea that ‘death is part of life.’
Bug/Dragon would be either crazy awesome or incredibly stupid. Sometimes these things are too close to call.
Ghost/Steel would be a b#$t#rd to kill because you just know it would get Levitate, but it could potentially go interesting places by shoving together the spiritual nature of the Ghost element and the technology associated with the Steel element (something Steel/Psychic hasn’t really explored, for whatever reason).
I think Bug/Water deserves an honourable mention because, yes, there is Surskit, but come on (I sort of find myself wishing Masquerain had just kept his original typing, because sticking the poor thing with Bug/Flying is just a tragic waste of a design that was actually quite fun). Dragon/Ice, too, might be fun to look at outside of a legendary context.
A correspondent of mine has hinted that he may be starting an art blog dedicated to exploring these unused type combinations in months to come; I’ll be sure to plug that if it happens.
Pokémaniacal 