Installed babylon in Firefox, now I can't get rid of it

You can try resetting all of the Firefox preferences to the default settings. According to Firefox's support page:

At the top of the Firefox window, click the Firefox button, go over to the Help menu and select Restart with Add-ons Disabled... Firefox will start up with the Firefox Safe Mode dialog.

For Windows XP, click the Help menu and select Restart with Add-ons Disabled...

1: To reset your user preferences, click to put a check mark by Reset all user preferences to Firefox defaults.

2: To apply your changes, click Make Changes and Restart.

Firefox will restart with your settings changed back to the defaults.

If the problem's only in interpreting misspelled URLs, do the following:

• Delete the babylon file in C:\Program Files\Mozilla\Search Engines
• Then open Mozilla and type about:config into the address field
• Filter for "babylon"
• Replace the babylon-setting in keyword.url with http://www.google.com/search?hl=en&q=
• Replace the others "search the web (babylon)" with "search the web (google)" and you're good to go.

I uninstalled Firefox, searched and deleted all references to Babylon in the registry, rebooted and reinstalled Firefox and the problem was solved.
Be advised that all bookmarks, cookies and passwords will be lost.

Here is what worked for me. I disabled it in Firefox add-ons (Tools, Add-ons). It would not let me uninstall it, so I closed Firefox and searched my entire c drive for babylon. I came across a folder labeled babylon and deleted it, as well as a .jss file. Once those were deleted I started Firefox again, and it was gone from my add-ons list.