There are several ILSes out there....and my library should know, since we're probably going to purchase one of them soon.
I think I've talked a little about Koha and Evergreen, the new kids on the block. They're both open source, which means that a couple of American companies have moved in to provide support for these free systems, for a nominal (!) fee of course. I've heard mixed things about the Koha support company, LibLime, mostly because they purport to support Evergreen, but in reality try to keep people from getting it. So all of their users use Koha. Equinox, which I believe was started by the people who originally built Evergreen, is the main supporter of Evergreen. There are a few other companies that support these open source systems, one in Canada, I think, one in France, a couple in Australia.
There are also the proprietary systems. From conversations I've had and overheard, people think it's a foregone conclusion that proprietary ILSes are going the way of the dodo. I don't know that i believe this. The systems themselves might eventually become obsolete, but these companies can just follow the path of LibLime or Equinox, and start their own open source support (LibLime certainly charges as much as a proprietary vendor).
The PVs (proprietary vendors) are: III (Innovative), Ex Libris, AGent (Auto-Graphics), Polaris, SirsiDynix, and Liberty3 (Softlink).
There are a lot of proprietary systems, although the numbers do seem to be dwindling. I was talking to my husband about the apparently anti-competitive behavior on the part of SirsiDynix in relation to Horizon, and he said "ah, but it's really just good business practice."
And he's right. All of these companies just do what they have to do in order to make money. Lots of library people (and the library vendors) like to talk about how they're all just librarians at heart, and they really want what's best for us. But in actuality, they're just a business, and they want to make money. That's their real mandate. All the rest is just fluff. And I think that the third-party vendors who are riding the wave of open source software will end up the same way--in it to make a buck.
But hey, this is America! That's why we're all here.