Been discussed MANY times before since people want to be rewarded for running a full node as some kind of "node reward". The short answer is: It's impossible. There's no way to prove you are a real node relaying real transactions or data without some "proof of work" - and guess what, "proof of work" is precisely what mining is. Then there'd be exactly the same arms race there is for regular mining rewards as there is for node rewards, the node rewards being in essence an altcoin built on top of the existing bitcoin, making it not worth mining "node rewards".

Id rather use my CPU cycles for something else though. I will pay for my node(s) as long as I can afford it. Its a worthy investment even if its just for the knowledge gained. It also allows me to do things I wouldnt be able to do without them, e.g. generate my own stats or consistantly rebroadcast unconfirmed TX from a well connected 24/7 node.

Nothing is imposible but for such a thing to be viable we'd first need a way to accurately know which nodes are contributing nodes and which are fake/imitators. A reward would surely attract the latter. Now, embeding such a reward into bitcoin's protocol would be a whole other story as it would require a fork and the agreement of miners.