I know they saw 3/4 in MDF is recommended, but what is the thinnest wood I could use to build a box for a 12" sub?

 

3/4"....if you use anything thinner with a "good" sub your gonna split the wood right in two.

 

3/4 only. Even 5/8 ends up flexing without proper bracing.

 

5/8 is ok to use. just add a little bracing. its its a powerfull sub then use 3/4 or even bigger. but if its and entry level 100-300wrms sub 5/8s will be ok. bigger is always better but your not going to blow anything up with a small sub. use good glue, lots of it, its cheap.