appmanager saves the apk install files to sd card. You then would have to use a file manager to isntall them again.
Titanium Backup free will backup the apps, your data, and even os data (though you won't always want to restore that, depending on what ROM you put on). This needs root, but that shouldn't be a problem if you are flashing a custom rom.
The restore function on the free app requires you to click install then OK for each app you reinstall. The paid version will automate that for you.
Nandroid backs up EVERYTHING so you can restore your phone in one step as if you never flashed it at all. Doesn't help if you want to keep the new rom but restore some settings.