How can I forward SMS via Jabber (XMPP) to read them on a PC? I want my received SMS to automagically be forwarded via Jabber (XMPP), so I can read them on my current PC.

I don't want to send SMS from my computer, though I would not mind the feature as an extra bonus.

How can I achieve this?
GTalkSMS (Google Project Page) does what you want (and much more).

Edit: After actively developing GTalkSMS, I decided that it's time to spawn a new project called MAXS. See my second answer.

Note: According to the FAQ I have to disclose that I am involved into GtalkSMS. GTalkSMS is an open source GPL licensed Android app. Everyone can contribute.