The most obvious vocal effect is the singing style itself, and different musical idioms often develop their own style (e.g. jazz, blues, and so on). In the classical repertoire, style is closely linked to historical period, and choirs (and soloists) tend to specialise in a particular kind of singing. Such issues as the amount of vibrato used and the way trills are executed will often be determined by stylistic concerns.
Speaking is frequently used in vocal writing and there are choirs which specialise in choral speaking. Sprechstimme or Sprechgesang is half-speaking, half-speaking, and probably the most famous example of this is in Pierrot Lunaire (1912) by Arnold Schoenberg. In addition, singers may alter the shape of their mouths to produce a different sound quality: closed, half open, and so on. Humming and whistling are two more common effects, and the direction sotto voce indicates a 'sung whisper'.
In much 20th century vocal music, other vocal sounds have been explored, and really the only limit is the composer's imagination. It is often helpful to use the phonetic alphabet when the texts step outside known languages. Theatrical effects and dramatic gesture can also often be highly effective, depending upon the context for the performance.