Most Common
Considering the three top used Pokemon in OU at the moment (according to this) are Talonflame, Charizard, and Heatran, I would have to say Fire is the most common type. But upon reconsideration, I have to disagree with my earlier opinion...
To be honest, the most common type might be Water instead, as Greninja and Rotom-W are very common Pokemon (#4 and #5 on the previous list), but there are also a lot of other Water types used - Azumarill, Crawdaunt, Gyarados, Keldeo, Vaporeon, Quagsire, etc. Whereas there are few (if any) other Fire types used than the 3 mentioned above.
And then Qwerty Zoom reminded of the Steel type. This type is the best defensive type in the game, and has many very common Pokemon in it. Even with Aegislash banned, there is still Scizor, Ferrothorn, Mawile, Skarmory, Excadrill, Bisharp, Heatran, and Aggron, all of which are very common Pokemon in OU (well, not Aggron quite as much, but it is still good). In fact on my previous source, 8 of the first 20 Pokemon are Steel types. While that does include Aegislash in it, it still says a lot about the power of Steel types in general.
Least Common
I'm not sure about the least used type. Maybe Normal, as the only common Normal types I can think of are Ditto (and does that even count?), Smeargle, and Staraptor. Actually maybe Chansey/Blissey are used enough it isn't Normal, but I really don't know.
As DarkHeart pointed out to me in the comments below, Bug and Rock are other good contenders for the least used type. For Bug, Scizor and Pinsir are very common, but the only other Bug type ever really seen is Forretress. Rock only has Tyranitar as being very common, but some other Rock types that are sometimes seen are Terrakion and Aerodactyl.
All of these less-used types have 1 or 2 common Pokemon, and then several uncommon Pokemon used, so I think it might be very close between the 3 as to which is used the least.
Conclusion
Sorry for the continous edits, but there are things I keep not considering. At the end of the day, I have given no clear answer. However, as the most common type I argue it is probably Steel, with Water as a close second. For the least common type, it is probably Normal or Rock, with Bug close behind. Finally, I hope I can stop editing this answer :)
