I believe it is advertised as unlimited,
E.g. in 2007 Facebook Photo Storage was as follows
Allow me to geek out and share some
photo infrastructure statistics with
you. We have:
1.7 billion user photos
2.2 billion friends tagged in user photos
160 terabytes of photo storage used
with an extra 60 terabytes available
60+ million photos added each week
which take up 5 terabytes of disk
space
3+ billion photo images served to
users every day
100,000+ images served per second
during our peak traffic windows
This month, the Facebook Engineering Team talked a bit about the messaging platform on their blog
Since Messages accepts data from many
sources such as email and SMS, we
decided to write an application server
from scratch instead of using our
generic Web infrastructure to handle
all decision making for a user's
messages. It interfaces with a large
number of other services: we store
attachments in Haystack
And Haystack is currently being used for Photos.
Though if you start racking up tens of gigabytes, it will get ugly.