Strictly speaking, the conjugations of 得る are: - negative: えない - masu form: えます - te form: えて - terminal form (i.e. at the end of sentences, or when attaching to べき): える／うる - attributive form (i.e. akin to such things as すきな for すき; used when attaching to nouns): うる - conditional form: うれば
It is the only 二段 (nidan) verb from old Japanese that hasn't fully become an 一段 (ichidan) verb in modern Japanese. (える／うる in old Japanese was う, so it has changed a little already.)
In summary, although うる is a more archaic way of saying える, the only time you can choose between える／うる is when it comes at the end of the sentence, or when attaching to べき (in which case, however, うる is also preferable due to the also archaic nature of べき). This means one should say for example うるために, うるように, うること, うるところ and so on. Additionally, ありうる is never ありえる.
However, in practice, the "wrong" forms are still somewhat often used.
Make that 'sometimes' ;-)
Rather easy to get confused with uru 得る - often used in the same way (see ariuru vs. arieru)