I don't like it, but so many people use it and trust it.
There is another one too, KeepPass I think. One is better for online the other is better for offline. Or so I read.
I have been using it for months now and have never had anyone steal my passwords. There are a few different ones out there but I like lastpass.
keepass is quite good, and it also has a LOT of different os's that it has ports for, so its nice if you have an iphone or an android device etc.
my gf just had had 600$ stolen from her paypal account (getting the funds back of course), so have been in the process of changing all of my and getting her to change all of her passwords just to be safe, apparently facebook, twitter, paypal, and a few other sites have had their userbase exploited
http://www.cbc.ca/news/canada/prince-edward-island/story/2011/06/17/pei-lulzsec-personal-internet-accounts-584.html