Your license should be compatible with the GNU GPL, current version or later. (This includes LGPL-only, since all LGPL versions can be converted to any version of the GPL. Of course, we strongly recommend against using LGPL-only. And GPL*-only is not acceptable.)
Your license should be compatible with the GNU FDL, current version or later.
We accept any free license for images and other data that are a secondary part of a package that is mainly software.
In any case, you cannot rely on incompatible dependencies.
These licenses are the ones that the GNU project uses for its own packages, and recommends for everybody else to use. They are also the most widespread, and being incompatible with them is a practical problem, because you would then be unable to combine code under those license with yours, and vice versa, even if it is free software.
Well-known licenses compatible with the GNU GPL are listed at http://www.gnu.org/licenses/license-list.html#GPLCompatibleLicenses.
Informal materials, FAQs, and so on can be under a license compatible with either the GNU GPL or the GFDL (or both). Manuals themselves needs a license compatible with the GFDL.
In some case, it may be useful to dual license your application - that is, release it under two different licenses - to meet this criteria. See DualLicensing for details.
https://savannah.gnu.org/forum/forum.php?forum_id=4303 describes more rationale with respect to requiring the GFDL for the manuals' license (and needs to be merged here).
Your project dependencies also need to be compatible with the license you chose. This is not a Savannah-specific requirement, because doing otherwise would make your project legally inconsistent, and as such not freely usable.
For example, a project released under the GNU GPL may not be combined with code licensed under the MPL, because those licenses are incompatible. However, you can combine GNU GPL'd code with code released under the Expat license.
email@example.com, that is, the FSF Licensing Team, may offer suggestions to find the best way to handle legal issues.
For non-software, non-documentation works, when we say "free" this refers to http://www.gnu.org/philosophy/free-sw.html. Licenses listed as "free" at http://www.gnu.org/licenses/license-list.html (whatever the kind of work) are good examples.
http://lists.gnu.org/mailman/private/savannah-hackers-private/2005-July/000142.html (private archive) is the discussion thread with RMS about that point, and is summed-up in the previous sentence.
Fonts: there's an interesting article at http://www.fsf.org/blogs/licensing/20050425novalis