Yes its possible, after trying to watch my favorite youtube videos on my Blackberry i decided to search for an alternative and i"ve found one. Go to your Blackberry App World and search for and download vuclip, now if u see a video that you'd like to watch on youtube, get the title of the video and open your vuclip (it uses your BB browser by the way) and put the title in the search box, it"ll bring up the same video from youtube, you can stream or save it to your device. You can also search directly for the video in the vuclip search box without first getting the title from youtube, but that"d be too cumbersome as vuclip is also connected alot of other sites and it may take a lil while before you find the video you are looking for. Try it and let me know.

P.S: its not really free, you must have BIS subscription for it to be free, otherwise prepared to be billed heavily, so make sure that you"ve subscribed to your network's BIS. Cheers