Lets make this a proper answer: There are a few possibilities to detach adherent cells without Trypsin.
PBS/EDTA: Integrins and Cadherins play an important role in the adhesion and also in maintaining cell-cell contacts. These function of these proteins depends on Calcium2+ ions, so EDTA will chelate them and make them unavailable. First remove the culture media, rinse the cells with warm PBS to get rid of most ions and then incubate them for 5 min (the time needs to be optimized for each cells line) in PBS with 10mM EDTA in it. The cells either detach themself, can be washed of the surface with a pipette or can be gently knocked off the surface (this works only in tightly closing flasks). Centrifuge the cells shortly to pellet them and get rid of the PBS/EDTA and take them up in fresh medium.
Wash cells of the surface: Some cell lines are so loosely attached (which makes working with them pretty hard), that they can simply be washed off the surface. To do so, use the pipetboy to get some medium and then pump it out again against the cell layer. You can see the cells disappearing from the surface and the medium (or the PBS) get more cloudy.
Knock off cells: To do so, you take the flask with medium in one hand and knock it gently 4 or 5 times against the palm of the other hand. The cells should come off then and can be centrifuged down to separate from the medium. Alternatively you could replace the medium first and then knock them off. This method is not recommended for very sensitive cell lines.
Besides these methods, there are a number of commercial products available which claim to be better than the classical Trypsin/EDTA method and to be less harmful for the cells. Since I haven't tested them, I cannot say anything about them. In my experience Trypsin and the methods described above work perfectly.