Clipboard Recoder.
http://www.lw-works.com/
Unicode is a must for me. ClipX and Ditto also support unicode. Ditto is kind of resource-heavy (for this kind of software) and can't display some unicode characters properly. ClipX sometimes loses "clip-chain", and it's a pain to kill and restart the program just to regain it.

Clipboard Recoder is lighter than ClipX and doesn't take focus away from, for exmaple, in-line renaming in Explorer. Try it!

Hi,
As an alternate clipboard extender, you might consider CLCL. I see it's already in the database:
http://www.portablefreeware.com/?id=469
It may probably seem "ugly" interface and tricky to understand all the options, but once you have it behave as you want, it's a great timesaver.
I'm not sure about Unicode, but developer is Japanese, so I guess it should work. Website:
http://www.nakka.com/soft/clcl/index_eng.html
I see in hist website that there is a plugin for Unicode:
* fmt_unicode Ver 0.0.1 (2005/02/11)
o Unicode Text Format (Windows NT4, 2000, XP and later)

Thanks for your reply, jordis. I did try it in the past, although I didn't mention it in my original post. The only drawback is unicode. You can deal with only one unicode clip at a time. You have to open the main window to explicitly call for that plugin. This was the deal-breaker for me.