How many "main characters" (ie Pokémon you like to keep at roughly the same power) do you put in an average playthrough...?
Dozens.
Right at the moment, in Black 2, I've got 28 in my main box and the six on my team, so 34 total. I'd potentially have even more than that, but I'm close to filling that box, and I don't really want to expand out to two "first string" boxes, so I've been dropping some down to auxiliary boxes along the way.
...and how does that affect your experience?
To me, it makes it more fun. I love using lots of different pokemon and lots of different strategies, and get bored if I just keep using the same few over and over.
For instance, earlier today I got to Victory Road and met N, so I got the Waterfall TM. I went through Route 23 with a premier traveling team - Crobat, Scrafty, Excadrill, Vaporeon, Leavanny and Chandelure. But since I'm going to go back now and explore all the waterfalls I passed up, I'm going to swap in Azumarill and build a different team around him. Probably take Swanna, since she's got both Surf and Fly already, and I'll want a Psychic since Swanna's a bit weak and can't handle all the Fighters on her own (and that'll probably be Reuniclus). Yeah, and put Krookodile in the Ground slot, and he can handle Dark duties too. Take a fast Fighter - probably Mienfoo (who's pretty close to evolving). And since I'll be spending a lot of time on water, I'll want an Electric or a Grass - probably an Electric, since I'm going to have two Waters along to handle Grounds and Rocks. I could use some bulk, so Magnezone would be good. And boom - there's an entirely new team, with an entirely different set of pokemon, for an entirely different purpose. And when I get done doing that, I'll put together another team for whatever I'm going to do next. That, to me, is fun.