A prefix, originally the same word as by;

To intensify the meaning; as, bespatter, bestir.

To render an intransitive verb transitive; as, befall (to fall upon); bespeak (to speak for).

To make the action of a verb particular or definite; as, beget (to get as offspring); beset (to set around).

The English derivational prefix be- is a hold over from Old English. For the majority of native speakers the prefix be- is no longer productive; a possible exception to this is presented by the word besmitten, which numerous speakers seem to have recreated http://www.worldwidewords.org/qa/qa-bes2.htm. Meanings and uses of be- include: thoroughly, excessively, or more generally, used as an intensifier; on, around, over, or generally indicating contact; finally, it is also used to form transitive verbs from nouns (e.g. befriend, behead, benight), adjectives (e.g. bedim, bewet) or otherwise intransitive verbs (e.g. bewail, beweep).