A facebook fanpage thingie is good, IMHO, because people can like it and share it and it spreads... A few artists on here have both a personal page and a fan page and I kinda wonder about the personal page, because you would be inundated with friend requests from dA fans.....
Not only do I have one but I have a Fanpage set up for my comic.
It's definitely a way to tag another group of folks. I know people who live on FB. I also know folks who don't care for it and live on Twitter and Tumblr. The ability to cross-post from one source to the rest is always a plus as I can post to my fanpage and have it hit Twitter or start from Tumblr and have it sent through the whole chain.
Blanket the networks. Leave no fan alive... er, "uninformed"! = P
Yes I do have one, but it's a "personal" page not a "fanpage" one. Well... I think it's a very good idea to show your works.. but as it happens with tumblr.. it's not a very trusty place. So I recommend you to put watermarks on your works. ^^
I have a fan page for my own art/shop and from what my fans have told me, they love seeing what I'm working on (When I actually remember to take pictures of my work, which reminds me...). Either way, it's up to you. :3 People can share your page on fb, further spreading the word of you, and giving them some sneak peeks that way or even updates on your thoughts and such are a good way to show that you're alive. ^w^
From a professional standpoint Facebook is a very good idea. It's basically just another way to network, but it gets your work out there. If you make a fan page, you only have to put information you want other people to see.
It's up to you, but know that any information you put on there is on there forever for anyone with the right skills to see. The people that abuse facebook are able to look at any information you put about yourself on there, regardless on whether you add them as a friend or not. I never got myself a facebook, because I'd rather spend my time doing things other than checking my status and publishing my personal information for all to see. IMO Deviant art is better since you are judged by the art you make instead of your identity. Again, its up to you. Just know that you can't take off any private information you put on facebook, since it stays on the facebook servers forever and can be used by the people who own facebook for whatever purpose they choose, including selling it to spammers.
We have a personal account and a fanpage for us as artists. We personally find it useful to promote ourselves to a wider audience and our personal accounts are great for saying in touch with far away friends. We use ours everyday.