Starting with the poll at the bottom of Turning and Churning, it appears that Turn Undead was essentially the same through D&D, AD&D, and 2nd Edition D&D, with changes for 3rd and fourth edition.
Looking then at the Advanced Dungeons & Dragons® Player's Handbook Turning Undead Section we see the baseline rules for that edition.
If the number rolled is equal to or greater than that listed, the attempt is successful. If the letter "T" (for "turned") appears, the attempt is automatically successful without a die roll. If the letter "D" (for "dispel") is given, the turning utterly destroys the undead.
Also D&D Class Roles – The Cleric covers the significant differences between the cleric class in general and states:
At higher levels, clerics used to be able to use their turn undead features against demons and other evil outsiders
For 3rd edition we can simply look at the SRD:Turn or Rebuke Undead. General changes are that demons and other evil outsiders are no longer mentioned and the table has been significantly simplified to include simply the resulting number of hit dice turned or destroyed.
If you have twice as many levels (or more) as the undead have Hit Dice, you destroy any that you would normally turn.
Wikipedia also provides some information on the difference in the cleric class across editions and in 4th edition
clerics possess the "Channel Divinity" class feature and can use it for multiple functions, including Turn Undead