Rhianna posted a comment that gave me a kick in the brain. Along with everything listed in the previous post, you will need copies of orders, marriage certificates, divorce decrees (if applicable), birth certificates for all dependents, AND MAKE SURE YOUR MILITARY ID WILL NOT EXPIRE WHILE YOUR SPOUSE IS DEPLOYED!! I'm sure there is a way to get your ID renewed while your spouse is deployed but I'm also sure it's a major PITA. Much easier to do if your "sponsor" (Gosh, I hate that term - makes me sound like I'm in a 12-step program...) is able to go with you.
Anyway, Rhianna's comment reminded me about POAs...Power of Attorney. There are several different kinds that JAG can draw up for you or you can be like me and have them write one specifically for you. Sometimes JAG is a little less than willing to draw up the kind of POA I ask for - I suppose too many spouses have abused the power that is granted in said POA and taken advantage of their soldier (and their finances) while they are deployed. My mother raised me better than that (I actually made that comment to a JAG employee that was drawing up my POA and he laughed). The POA that I have grants me the ability to pretty much do anything - essentially, I can do everything except have McGyver's wisdom teeth removed without him being present. I can open banking accounts, establish investments, take out loans, accept housing and delivery of household goods, schedule pick up of household goods, buy and sell cars in his name, buy and sell a house in his name...you name it.
Now, POAs do not HAVE to be accepted by any financial institution (and I've run into a few that will not - they no longer get my business) but you're better off having one. They also are necessary when dealing with Finance in case there is an issue with pay while the spouse is deployed.
I think my POA (and my military ID) is one of the most valuable pieces of paperwork I have in my possession.
Just my $.02...