The banjo is a fine instrument (I just bought a Mike Ramsey Fairbanks Electric today) and I love it - but I wouldn't say there's no social stigma. Most of the banjo jokes I've heard were from Americans. Maybe it's because the banjo is a potentially loud instrument, which can sound REALLY AWFUL if played badly.

I've heard a joke attributed to Mark Twain that the definition of a gentleman is someone who owns a banjo, but doesn't play one. I looked it up and discovered that the attribution is dubious, but we do know Twain said this:

"When you want genuine music--music that will come right home to you like a bad quarter, suffuse your system like strychnine whisky, go right through you like Brandreth's pills, ramify your whole constitution like the measles, and break out on your hide like the pin-feather pimples on a picked goose,--when you want all this, just smash your piano, and invoke the glory-beaming banjo!"
   - Mark Twain, "Enthusiastic Eloquence,"
    San Francisco Dramatic Chronicle, 6/23/1865

To paraphrase Bruce Phillips, I would call the banjo "loved but unrespected." On either side of the pond.

Dan Schatz