Are you trying to download a new release or a really popular video? There have been a lot of new fakes around lately... new releases, heaps of sources (up to 100) per file, 4 star connections. These things will sit at 'connecting' forever. Try to download something with less than 10 sources. Vary your search terms & try the All Types search. Look up a file before download with Bitzi
How to use Bitzi

(mmm but there's also a bug in some versions which causes this to happen
http://www.limewire.org/forum/showthread.php?t=84)