I do, quite a lot:
- This was my main reason for buying a PS3. I had bought countless japanese PS2 games and no japanese PS2, so no way to play them. I bought a japanese PS3 to enjoy those games, and my original PS3 has been used more with PS2 games than with PS3 games. I bought a slim later, so of course this one was PS3-only.
- I truly love playing old games. My SNES is always plugged and ready to run, and I use it regularly. PSOne, N64, even 8bits consoles are getting some use. Problem is, with the increasing number of hardware failure, I should buy at least two of each consoles to make sure that I will be able to play my games in half a dozen years, which is expensive. By having BC, this need is lowered (for GC games, I have GC and Wii, for Wii games I have Wii and Wii U, etc., so if one broke, I'm not out of options).
And the number of consoles that I have to keep plugged in is lower.
But if it becomes a truly big issue to manage BC, I don't have a problem with a console maker ditching it. That's just very, very convenient.
(btw, if the 360 had better BC, I would probably have bought one just to play the XBox games I never had the chance to play. With PS1/2/3 and Nintendo consoles, I'm not missing enough games to justify a third one each generation, but having a way to play XB and 360 games in a single package would have proved a sufficient reason to buy a 360)