As of Monday Feb 15, passing a User-Agent header is mandatory for *all* HTTP requests to Wikimedia sites. This includes the API. If your client doesn't provide a User-Agent header, it'll receive HTTP 403 errors with the text "Please provide a User-Agent" or something along those lines. This was announced in a (now rather lengthy) thread on wikitech-l: http://lists.wikimedia.org/pipermail/wikitech-l/2010-February/046777.html
Ideally, your User-Agent header should identify your client in such a way that Wikimedia staff are able to figure out who to contact if your client is somehow engaging in disruptive behavior. Putting in an e-mail address works well for this, but mentioning your wiki username, the name of the wiki page of the tool (with wiki prefix, so they know on which of the 812 wikis to look) or a URL to a page about you or your tool are fine too, provided that they lead to a functional way of contacting you.
Please don't take this as "if I set a User-Agent my client will potentially be blocked". If it's being disruptive, it'll be blocked anyway; if you set a User-Agent header, you'll be informed immediately, or better, get a chance to fix your client without having it blocked.
Roan Kattouw (Catrope)