Why not? I've been using it for about a year now (switched from LastPass) and haven't had any issues. Kind of miss the in-browser features of LastPass, but seeing as how those are what's being exploited, maybe not so much!
There are browser extensions that work with KeePass. This LastPass vulnerability makes me wonder, too. I wish the KeePass site would be 100% HTTPS, though, but the maintainer is a jerk in that regard.