KeePassX has similar "auto-fill" functionality as well. It's not as perfect or as seamless as LastPass but it is definitely usable (after a bit of one-time per-site tweaking in some cases). Having recently decided that using LastPass presents a non-zero risk, the extra effort I have to spend w/ KeePassX is certainly worth it, IMO.
Although I don't do it now, I have in the past kept my password databases in Dropbox. With Dropbox also installed on my iPhone, I am able to access my password databases use "MiniKeePass" on iOS without any issues.
In addition, there are Windows, Linux, and OS X versions of KeePassX and all of them can open up my .kdb files without any issues.