after it's all said and done, do what works for you. though i'm not sure how long you've been working out, so i'm not really sure how much help that does.
many nutrition guides and weight lifting/training "gurus" feel that you get the best "bang for your buck" if you take it after training. biochemically, your body will do what it needs to do in order to heal and build the muscles... technically, you could eat a bunch of lard and your body would try to take the components of that and use it to make protein. the problems that would arise would be 1. the caloric content of lard and 2. the lack of nitrogen (thus requiring the body to get the nitrogen from elsewhere, which would require amino acids and protein... but i digress). it seems to be best to take a protein shake after the work out because the body can take the components of the shake and use them immediately for muscle repair and growth.
as far as what to do on your off days, it depends on how you live. for me personally, i try to do nutrition bars or shakes every day because it keeps my calorie content low as compared to the way in which i like to consume eggs (a little milk, a little cheese, etc. etc.). for me, protein content wise i'm better off using shakes or bars because i can get a little crazy with other sources of protein content.
if you have good diet discipline, then utilizing other sources of protein (as skier pointed out) is good. if your diet discipline is lacking, or you just like protein shakes, then i would suggest to continue to use them.
just for fullness of info, whey is from eggs, casein is from milk. many people suggest casein at night because the body takes a bit longer to break it down, i.e. it's a bit slower to break down metabolically.
just the opinion of one med student, who likes to work out
