When I first started out in competitive battling, I would make teams of fully unique pokemon. :/ But that's because I didn't know what was good and what wasn't. I didn't know about tiers and the like.
Now, I feel originality is a minor part of the game itself. Don't get me wrong however, I'm an originality freak when it comes to most games, but originality in this game comes at the cost of losing powerful pokemon (most of the time).
Usually I go for pokemon that perform well together and sometimes that strange pokemon can work its way into my team. It's just a little too minor for me to actually worry about most the time, honestly. But that's only with this specific game. Any other game and you'll see me using strange things (namely the Call of Duty franchise. Online, I'll use some of the least common guns and they work wonders for me, but others prefer to join the crowd and use the most common guns at the time).
I do try to look for unique sets for pokemon though, or at least change a few things up from the Smogon sets. :/ My main example would be Rotom-C and putting HP[Fire] on him, which is not suggested by Smogon for the set I was using. I only put it on my team because I had no Fire type attacks, and since Scizor is so common, I knew it'd come in handy. Now Rotom-C is the star of my team and HP [Fire] is probably my most used move (out of Leaf Storm, Thunderbolt, and Shadow Ball).