Does "The Hobbit: The Desolation of Smaug" have spiders in it?

Yes - there are giant spiders in the film for a decent length of time.

For a more detailed account (which contains some spoilers) see this IO9 article which sums up the first 20 minutes of the film.

Despite your phobia, it would appear that these beasties are fantastic enough for you to brave them. After all, they don't really have any bearing on everyday spiders here in the real world.

Good luck.

EDIT:

I saw the film last night, and although I didn't have a stopwatch going at the time, I didn't feel that the spider sequence went on for much more than 12 minutes tops. It is actually pretty surreal and really well done, and adds a lot to Bilbo's character - however, the spiders themselves are brilliantly rendered and creepy, so if you really do have a strong phobia about them I would suggest just skipping the film.

I saw the film on the 15th of December, and I have arachnophobia as well. I thought the spider scene was really no problem for me.

At some scenes I laughed at the spiders and how Bilbo becomes more brave and confident as the incident with the spiders progresses.

There is a moment were Bilbo drops the ring he goes to pick it up, but then a weird withered giant bug appears from the ground. At first I thought it was a beetle of some sort but as I remembered in the book I thought that it could have been the elder spider.