You don't have to kill anything, you can choose to avoid enemies. Myself, I do prefer killing all the monsters just in case I have to retreat. On the other hand, a lot of people play the Sorceress just because she can avoid 90% of the combat and teleport to the Act Boss and kill him without having to face the hordes in the levels above.
You can also choose to do areas over again if they have monsters that are close to your level, as that will provide maximum gains from the experience points you can earn from them. Tristram and the Canyon of the Magi are popular places to do repeatedly for low level characters. Most people, especially on Battle.net choose to run pretty much only Baal because he and his minions provide the maximum experience.
Everyone and their brother wants to have a couple angelic sabers.