It sounds to me like you should be ok, though there is a limit on some rims for the width of tyre. Going from 700cx38 to 25 might be too big of a jump depending on the width of your rim (see Sheldon's page already referenced). And yes, I'd get new inner tubes as well -that's not to say your existing ones might not work, just that I'd be conservative with something as crucial as the interface between you and the ground. Better to get the right size.
A little example here, I looked at putting 26x1.25s on Sun Rhynolite rims, but decided the rim was just too wide. You've got to do a little eyeballing here and use common sense -again, err on the cautious side!