How much space can your BitBucket account have?

EDIT #2 (Over three years later, as pointed out by matchew)

As of 30 May 2014 There is now a 1gb (soft 2gb hard) limit. read this for more information

Here is a link to their FAQ which address this question

According to the banner on their homepage: Unlimited disk space. Ican highly recommend it. ;-)

* EDIT (ALMOST TWO YEARS LATER) *I can still highly recommend it ;-)And in the meantime they have addressed this question in their FAQ

We don't place any limits on the size of your repositories, file uploads, or the number of public repositories you can have. Not on the paid plan or on the free plan. We do expect that you are polite and respect fair use. read more....

Bitbucket's documentation says:

We don't place any limits on the size of your repositories, file uploads, or the number of public repositories you can have. Not on the paid plan or on the free plan. We do expect that you are polite and respect fair use. If you push your entire MP3 collection that is not polite or respectful to the artists.

^{(Just for the sake of completeness)}

Note that Atlassian changed their policy on May 20th, 2014 for newly-created repositories:

Soft limit of 1 GB – In-product and email notifications will give you a heads-up that you’re approaching the limit.

Hard limit of 2 GB – Pushing to the repository will be disabled until you’re back under the limit.

From their Repository size limits blog post.