Is multiboxing allowed?

If you're looking for a clear-cut yes-or-no answer from Blizzard, unfortunately you won't be able to get it at the present time; every recent inquiry about the subject on the official forums has been met with a generic "read the ToS" response.

There was, however, a post earlier this month by Blizzard representative Omrakos (in a forum thread that has since been deleted) that stated the following:

Multiple copies from the same number of multiple computers with the same number of multiple accounts will be fine. You can't, to my knowledge, run more than 1 copy per pc simultaneously though. - Omrakos

Therefore, I think the best stance to take is such: there's no guarantee that multiboxing won't get you in trouble, but as long as you're using separate computers and not running multiple copies on a single machine, you're probably somewhat safe. That's still not a guarantee, however, and Blizzard could change their minds at any time.

From a World of Warcraft and Starcraft 2 perspective, Blizzard has long allowed multiple accounts to play simultaneously.

The only concern is that you are careful if you are using software to play multiple characters at once simultaneously. Anything that emulates botting (keyboard emulation, packet duplicating, etc) will most likely result in bad times.