Most of the prime examples that have been mentioned already (New York Dolls, Cramps, Bowie, etc) I would like regardless of Morrissey. I actually hadn't heard anything by New York Dolls until after I heard that Morrissey was such a big fan, but I know that it's something I would have liked if I'd just been lured that way before (and I'm pretty sure that I would have by now). I'm also a really big fan of '50s rock & roll and rockabilly but, again, it's got nothing to do with Morrissey's influence.
'Meetings With Morrissey' influenced me to listen to some of the '60s girl groups that Morrissey adores and I doubt I would have ever done that if I hadn't read that book. I do actually like a lot of it, but it's not something I listen to regularly.
Being a second generation Syrian living in London, about a year ago I thought that it was time to start taking an active interest in music from the Middle East. Not knowing anything about music from that part of the world I went back to the statement that Morrissey wrote defending himself against accusations of racism because I remembered that he listed some Middle Eastern artists that he was a big fan of. I've since tried out some of those names and so far I've liked them all.