Deal with badly written code

Since I want to be a good programmer, I developed a precise coding style, and I do my best to write elegant code, however from time to time I find myself messing with poorly written code. This reduces my enthusiasm, and I feel the instinct of fixing it ...but in real life you don't have the time for fixing someone else's code, and you have to put a patch on it.

On the long term this leads to a world-wide growing code base which sucks and keeps sucking... and this drives me mad! How do you handle this problem?

tl;dr: We have a lot of shit to work with. How can you survive?

>>1
By abstracting it. Call into your abstraction, which looks nice on the outside despite housing that garbage that the coop student wrote.