Can anyone tell me if there are any services that use meta keywords, and if so, what those services are? I know that google doesn't use them, but I'm wondering if anyone else does.
I know that google doesn't use them
While it's pretty much settled that they're of relatively little value overall, this is not necessarily entirely accurate. If you pay attention, almost every time Google deals with this question directly(example), what they actually say is that they don't use them for ranking. If they were completely tossing them, that qualification wouldn't be necessary.
There's been evidence that they do index the keywords, even if they're not used for ranking. This would still make them useful for things like capturing searches for misspellings of your name, or related terms that don't specifically appear on the page, for example. I can't dig up the link at the moment, but this was tested by one of the search engine blogs some time ago by using a gibberish word created for the test that wasn't returning results previously. It would, of course, be easy enough to test this yourself.
There are also cases where they may end up using those keywords for deeper crawling via forms. (That link is to the main post; then scan for a comment by John Mueller. The Disqus commenting used there is making an anchor link to it flaky.)
Yes, eg. according to http://en.wikipedia.org/wiki/Meta_element Yahoo! still does. But in general, keywords in meta tag are losing significance.
Your competitors probably look at them to get an idea as to what keywords you're targeting.