I\'ve never actually used greasemonkey, but I was considering using it. Considering that GreaseMonkey allows you to let random people on the Internet change the behavior of your
Yes, userscripts can steal your passwords. That's the bottom line. Don't use firefox addons or userscripts on work or government computers without referring to your bosses.
Unlike firefox addons userscripts are not formally vetted. (Firefox 'experimental' addons are also not vetted). You can register and add a malicious script to userscripts.org in a moment.
Userscripts are very unsafe. The cross-site scripting ability means that it's no difficulty at all to send off your details/passwords to an evil server quite invisibly. And the script can do it for any site. Ignore the other answers that attempt to dismiss/minimise this issue. There are two issues: evil script writers putting their evil wares on to userscripts.org and scripts that break greasemonkeys' sandbox and so are vulnerable to being used by malicious code on a hacked site that would otherwise be restricted to same-domain.
In the case of evil script authors you can examine the scripts for code that sends your details; not much fun. At the very least you could restrict the script to particular sites by editing the 'include/exclude' clause. That doesn't solve the problem but at least it won't be sending off your banking credentials (unless you've used the same login details). It's a pity there isn't an 'includexss' clause to restrict xss requests, which would effectively solve the problem since, crucially, it would be easy to check even for non-developers. (the Firefox addon "RequestPolicy" doesn't block userscripts.)
Unsafe scripts: look for any use of 'unsafewindow'. There are other risky calls. Greasemonkey doesn't warn you of their use when the script is installed. Use of these calls doesn't mean the script is unsafe, just that the script writer had better be good at secure programming; it's difficult and most aren't. I avoid writing scripts that would need these calls. There are popular, high-download scripts that use these calls.
Firefox plugins/addons at Mozilla.org have similar problems to userscripts but at least they are formally vetted. The vetting/review includes the all-important code-review. Nevertheless there are clever techniques for avoiding the detection of evil code without the need of obfuscation. Also the addon may be hosted on an (unknown to anyone) hacked site. Unfortunately mozilla also lists 'experimental' addons which are not vetted and have had malicious code. You get a warning but how many know the real significance. I didn't until I picked up security knowledge. I never install such addons.
Userscripts are not formally vetted. Unless a script has a lot of installs I examine the code. Even so a high-install script could still have had the script-writer's account hijacked and script modified. Even if I examine a script the use of anti-detection programming means I may not see the evil. Perhaps the best bet is to examine outgoing requests with "Tamper Data" firefox addon, but a clever script will delay or infrequently send data. It's a tactical war, unfortunately. Ironically only microsoft's certificate based activeX objects really approach a real solution in developer traceability (but didn't go far enough).
It's true that a firefox addon gives an evil-doer greater exposure to potential victims, since firefox addons are generally more popular and so seem more likely to be targeted, but the firefox vetting process makes userscripts more attractive to the evil-doer since they are not vetted. Arguably a low-download userscript can still get a criminal plenty of valuable logins until it is spotted, while also giving the benefit of the relative obscurity and low community churn of userscripts, as well as a low chance of anyone code-reviewing it. You can't depend on firefox addons' popularity to protect you from evil userscripts.
As a non-developer you are dependent on other users spotting evil scripts/addons. How likely is that? Who knows. The truth is it's a crap security model.
Ultimately I use firefox for general browsing and Google Chrome (without greasemonkey/plugins) for admin purposes. Chrome also has a usable 'profiles' feature (totally separate browsing spaces) which is effectively like using different browsers. I've set up three chrome profiles to make myself even more safe: email/general-admin, banking, ebay/paypal. Firefox has unusable profiles (in my experience) but I prefer firefox as a browser which is why I still use it for uncritical browsing. Profiles also protect against old fashioned browser security holes and hacked sites, at least limiting their scope. But make sure you use different passwords. Another approach is a clean bootable ubuntu install on a USB stick for critical admin (see here http://www.geekconnection.org/remastersys/).
Jetpacks' special trust model, rather like the PGP trust network, which underlines the seriousness of this issue, should hopefully mitigate it. Jetpack is firefox's new kid on the block: a kind of super greasemonkey.