(Now I just stopped holding my breath. Ah, breathing is good!)
Go to a site with saved passwords e.g. http://news.ycombinator.com
Lastpass icon changes to show you have an entry. Click the icon, click "Show matched sites." Hover over the entry and you'll see three buttons: Copy username, Copy Password and More options.
I'm assuming these buttons don't work for you. Right-click instead on the entry and you should see a menu with the following items: Autofill, Copy username, Copy password, Copy URL, Go to URL, Edit, Delete.
Try the copy password entry. Hope it works for you.
Years ago it was Hamachi (the LAN-over-internet software). Then it was LastPass and via it XMarks (itself acquired by LastPass shortly before). XMarks suffered much more grievously than LastPass — I suffered data losses on multiple occasions before finally throwing in the towel.
password-store uses git+gnupg so backing them up is a matter of distributing the git repo. My git repo lives on each of my laptops and I have a 'central' host of it...so it's backed up via distribution.
For getting passwords to my phone I use a homemade Android app + small web app that sends them to my phone encrypted on-demand from my laptop or desktop. There are Android apps for using password-store but you have to put your GnuPG keys on your phone for that and I prefer not to do that.
UP (uncle post) mentions a home-made Android app to sync... is there a more mainstream option?
But overall, yeah, it has been better than LastPass.
For a year or two, lastpass for Firefox didn't have the copy option for usernames and passwords. I had to edit, show password, then copy.
The autofill problem became pronounced after the acquisition as well probably through no fault of the new owner. Many sites like Google and Microsoft have switched to a multi-step login process where username is entered first and password is entered on a different page
Also a proof of sites abusing autofill & hidden forms to steal passwords probably influenced the current situation.