I have heard of companies paying off loans. I even worked for an engineering company where they helped pay off the general managers x-wife but I won't get into that
Personally I don't see anything wrong with wanting a company to pay off loans. Its all part of the negotiating. Maybe there are too many oldschoolers around here

Everything is negotiable nowadays. Company car, signing bonus, laptop to work from home, extra vacation days you name it. Even working from home one day a week. My wife's company is going to let them work from home one day a week because of gas prices.
Why would it be any different then your salary? What if you don't have loans? Should you get a higher salary? Should of thought of that before you signed your acceptance letter

Maybe they will have you sign a contract. We will give you a cash bonus for x amount of years of service. A signing bonus with stipulations.
Now, would I ask for them to pay them off? Nope (and I have ~70k). Only because everyone who posted here pretty much sums up the attitudes of most employers. I would do your research. If you are starting at 60k with little or no xp you would be pressing your luck.
Sorry for the rant but if you don't ask for it up front your probably not getting it later

Maybe its because I have usually worked for smaller companies (owned by large corporations) that I have seen some incredible stuff paid for on the companies tab.
I used to have my lunch bought for me just about everyday. 10 bucks a day adds up. Could of paid my loans at the time (before I went back for my BS that is)
Some companies are willing to pay tuition reimbursement. Thats even worse IMHO. I have friends who have gotten 30k+ from their company. What if they quit? Is it worth to go chasing after the person? With loans the government comes after you and garnishes your paycheck. The compnay wouldn't be any worse off helping to pay after they graduate. Then there is incentive for them to stay
Just something to think about from a disgruntled automotive engineer