Are there any risks to rooting a device?

Does it have the potential to brick the device?

Although it has become relatively simple on the Droid, some methods of rooting pose more risk than others. So in short yes there is a potential.

Will it void my warranty?

It mostly depends on where you live and on your manufacturer (and their warranty policies). But technically this does void your warranty in most cases.

Will I stop getting updates?

Again this depends. Some manufacturer provide updates for rooted devices while others do not. These will usually continue to come in and may unroot your phone if you install them, or even require you to unroot manually before you can receive their updates. If you install a third party ROM, then there's nothing else to do with your original manufacturer.

Will the cops show up at my front door the next day?

I certainly hope not :) but if rooting involves cracking a bootloader, it could theoretically get you in legal trouble in some jurisdictions (anti-circumvention laws, etc.)

EDIT: Also be aware that there are different root methods based on which current build you are running.

EDIT: It may (as of May 24, 2017) prevent you from installing some apps: Google Play can now prevent rooted users from downloading certain apps

Does it have the potential to brick the device?

Yes.

Will it void my warranty?

Definitely.

Will I stop getting updates?

Yes, if you install a custom ROM.

Will the cops show up at my front door the next day?

Yes, but only if you're Chinese ;-). And even then, only if your police administration is near enough to Beijing.

And you should be aware that it is a security risk. A root user has access to the entire phone, including all of its functionality, and the memory of all running applications. A backdoor could be installed in a custom ROM. It might not even be to your disadvantage, but your phone might become part of a botnet.

Does it have the potential to brick the device?

Yes, it is possible to brick your phone, but should be very unlikely. Usually there is a way out of even what seems to be a brick.

If you do not know what you are doing and want to use the ADB method (entering shell commands manually) to root your phone, then be sure to follow all of the directions exactly as listed. If you somehow brick your phone, then it does not matter how good your phone insurance is with your cell provider; if they find out you rooted or attempted to, they will not fix it.

If you do somehow brick your phone, then do not panic. Try these things:

1. Post a thread to where you downloaded the root program or where the root method was posted.
2. Post to XDA under their questions and answers section.
3. Search the web. Someone else has probably had the same problem as you.

It is quite possible to unbrick your phone, but it will take some time and patience to sort it out.

Will it void my warranty?

Yes. But in most cases you can restore your phone to a condition that they'll never know that you rooted your phone. And sometimes they do not even check to see if you rooted your phone when you return it.

Will I stop getting updates?

Yes and no. If you flash a rom, yes. But most likely that rom has constant updates (such as CyanogenMod). Also if you root and keep stock rom, you will still get OTA update notifications (but running an update will un-root your phone).

Anything else I should be aware of?

May the force be with you. No, really, it's a relatively painless process with a lot of these "easy one touch (un)root tools" and even then there is a plethora of guides and help from XDA to guide you and troubleshoot any problems you might have. But if you are happy with your phone just the way it is, then don't root.