When I was young(er) I figured the way to do this would be to coat the surface with micro-video cameras and microscreens. The light hits one side of you (your cloak, or whatever) and is instantly output on the screens on your opposite side. Effective invisibility. My brother tells me these are called 'null suits'. (A recent James Bond film made use of this ancient concept.)
This has the drawback of being difficult of working when there are multiple people looking at the invisible object (from different angles). Solvable by having the surface covered in tiny concave or convex spots covered in screens so people from different angles get a different view. This, of course, means the cameras and screens must be much smaller.
In Gene DeWeese's Black Suits from Outer Space series has the device make you transparent to visible light some how and draws the obvious (once pointed out) but oft-ignored fact that this means the light isn't received by your eyes: you'd be blind. This may have been the reason why invisibility in Quake leaves your eyes visible. Of course, in DeWeese's series the aliens who created the invisibility device could see a different spectrum of light. This way, they were invisible to humans but could still see when cloaked.
In Jay Williams' and Raymond Abrashkin's Danny Dunn #2: Invisible Boy they simply create a radio-controlled dragonfly, a more technologically advanced version of the 'invisibility' found in Edgar Allan Poe's The Purloined Letter (full text: zip, txt) or G. K. Chesterton's The Innocence of Father Brown.
I've constructed fully-functional models of each of these types, tested them, and am now ready to start mass production.