I just recently ordered a batch of business-card hang tags, but made sure to specify a heavier card stock so they aren't so thin. I plan on punching eyelets/grommets into them and hanging them from the neck labels with something. You should be able to buy the eyelet punch at some hardware/tool stores, along with eyelets of course; if not, Ebay is always there.
I didn't originally plan on going with business card sized tags though.
If you want to get fancier, consider looking into die-cut cards; you'd have to do the research though, I never looked into it much myself. It would be a little pricier though as they have to create a die (unless they have existing dies you could choose from). You could get some pretty cool shaped tags though, I imagine those places would also handle the printing unless you didn't want them to.
I even considered going with a grungy look, and using torn pieces of corrugated cardboard or something similar and punching eyelets into those. If you want something simply square or rectangular, consider checking out an art supply store. They would have heavier card stock, as well as all other kinds of fancy stuff you could use as well. Also consider fabric houses, hang tags made out of denim or other fabric are pretty cool. If you have a young brother or sister who wanted to make a little money, you could maybe set them up with a paper cutter and get them cutting out tags and punching the holes in them.
You could also handle the printing yourself in a number of ways, though you may be a little limited there. If you're fortunate enough to do your own screenprinting, or have a friend who does, you could print directly on whatever material you plan on using. Otherwise, you could do things like make a stencil and spraypaint your logo on, or even have a custom stamp made (check vistaprint.com) and just stamp them all. You may be a little limited to colors though this way, if that matters.
