My favorite has always been Lyra, though I don't get the whole "wants to be human" thing. Seriously, did I miss something? I also like Raindrops and Octavia and I would like Vinyl more without the glasses. Hopefully Octavia and Raindrops say something in season 3. My heart exploded when Lyra talked in the season 2 finale.
In one episode, it shows her sitting on a bench like a person. Kinda like the whole Fluttershy "Wants to be a tree" or Scootaloo being a chicken because she can't really fly kinda thing.
I forgot to mention that I also like Mrs. Cake and the cake twins. Not really background characters, but still I thought it was worth mentioning.
Cheerilee isn't really a background character. By now, she's more like supporting cast. I'm gonna say Vinyl Scratch and Derpy
My favorite is either Carrot Top or Pink Lady.... What, she exists... Still don't believe me? Check for yourself. http://mlp.wikia.com/wiki/List_of_ponies, just under Peachy Sweet and Prairie Tune. In the Apple family section. Reason why I like Pink Lady: http://www.youtube.com/watch?v=_pVX1fjOwNk Reason why I like Carrot Top: http://www.youtube.com/watch?v=QybkjWrL_ZM Rap has the potential to inspire a generation, if done right. Give a man lyrics and they can sing one song, Give a man inspiration they can make melodic masterpiece to inspire others..
I'd have to say Octavia on this one. She's not my all-round favourite pony, but she does top the favourite background pony mark for being graceful (or as Photo Finish would say, GRASHEFUL), sophisticated, an awesome looking design and colour scheme, kick-*** fan stuff about her, and her talent. Gotta love the bass cutie mark and the cello playing.