storing seed

Being a bit overly enthusiastic I bought loads of seeds, some of which I don't have room for this season, will they keep if stored in the fridge or does it depend entirely on what kind of seeds they are?

I have SO much seed left over (some of it because I get lots of freebies honest - well that's my story if the OH reads this!!) that I just don't have room in the fridge for it all.  Can I keep it in a box in the spare room hidden away from prying eyes who might see how much I have?!