I just took a look at LiveSearch and played around with it a bit. It can be integrated into WordPress with some hacking. If you now enter a term in the search form on the right, a list of search results will appear after a short delay - specifically the titles of the posts. This uses the normal WordPress search, so these are the same results you would get if you simply pressed Enter - just faster thanks to Ajax and as a direct inline list. Fun stuff. Should work with current IEs, Mozilla derivatives, and current Safaris.
However, strangely enough, the cursor keys for moving through the search results don't work for me, even though the code seems identical to the BitFlux page. Somehow it doesn't find the first line or something - very strange. But that part doesn't really interest me, so it doesn't bother me if it doesn't work.
Hmm. Safari works flawlessly, but my Firefox under OS X doesn't seem to work. Very strange. To be precise, it works with Firefox only after I delete a character with Backspace or press Space once. After that, it runs smoothly. Can someone explain this to me? Strangely enough, the cursor key navigation in the search results works with Firefox - if you have a list of results...
Update: strangely enough, the cursor key navigation now works in Safari. Something here is very strange ...