Apple has released 5.1. This is either being pushed out now or will be shortly. This has some bigger-than-normal impacts for jailbreakers. Please read this carefully.

There is no untethered jailbreak for 5.1. Do not update to it. You will lose your jailbreak, cydia, and all your tweaks..

Absolutely, do not use the onboard iphone software update to update your device. This will most likely render your device unbootable and you will be forced to restore to 5.1.

1) If you are on an iphone 4s or iPad 2, updating to 5.1 is one-way. (This may also be the case for iphone 4 users). You cannot revert back. If you try 5.1 you will be stuck there forever. You will not be able to jailbreak until a new jailbreak is released.

2) If you are on an iPhone 4 or ipad 1 or similar device, you will be able to jailbreak tethered, then install semitether to get a semitethered jailbreak. In short, this will be jailbroken but when you reboot, you will lose your jailbreak until you get back to your computer and rerun redsn0w.

3) If you are on an old 3gs, like always, you can jailbreak untethered.

Finally, some other issues to be concerned with. If you install something in cydia that causes your device to not boot, you have to restore, you will be stuck updating to 5.1. Therefore, I suggest you get SSH installed and learn how to use it. If your device is in an unbootable state, you can fix it via SSH. With SSH installed, you can get further help in our irc channel (irc.thebigboss.org, #ios).

Troubleshooting your device without restore:
If you encounter issues on your device like things are not running stably or such, rather than restoring, try to debug the issue. Here are my suggestions:
1) In cydia uninstall mobile substrate. This will remove many things. Allow that. Reboot the device.
2) After this, test the device. Is it stable? If so, move to step 3.
3) Reinstall one tweak of your choice. Only one. This will reinstall mobile substrate as well.
4) Test with just that one tweak until you’re satisfied your device is stable.
5) Repeat steps 3 & 4 with one tweak at a time until you find one that makes the device unstable. Remove that one only and continue on.