"老いる" means "get old," in terms of age as well as physical and mental conditions.
老いること isn't a desirable matter. But you cannot evade it. It's a rule of nature. Sometimes you can get wiser as you progress in age.
In that sense, "老いる," sui generis doesn't have so much negative tone as our Minister of Finance, Taro Aso thinks - He said recently in his public speech, "I don't understand why people over 90 of age wish to live longer," meaning, "they are done."
"老ける" means you "look old, or older than your age," possibly because of a longtime disease, self-indulgent lifestyle, or hard life. It has a negative tone.
When you hear "彼も老けたね - He looks aged” from someone, you'd sympathize with the guy he mentioned. But when you're told "君も老けたね - you look aged” in your face, you'll get shocked, and kick the ass of the speaker in return.
You cannot stop 老い, but you can fend off ”老け" by getting proper exercise, and staying young at heart.