I have recently married a man from another country. We are working on getting all paperwork straight, but have been told that this could take months to years to complete. Would having an ITIN number benefit us by filing taxes together? This number could help my health insurance cover him, but we are also worried that this might cause more problems for us than it is worth.

If you are a U.S. citizen or resident, then you can file joint return as resident even when your spouse is non-resident alien and has never been to the U.S. You can attach W7 (ITIN application) with your tax return.

Across the top of your return you write "spouse elects under sec.6013(h).
Then you compose a statement which both of you must sign stating that your spouse chooses to be treated as a US resident for tax purposes.

See Pub 519 and the section called "nonresident spouse treated as a resident" for details.
Publication 519 (2008), U.S. Tax Guide for Aliens