Date: 2/13/2009 10:10 am EDT
If you cover the top of the washer/ dryer cabinet you should adhere the tiles to the top due to the high speed and potential vibration of the front loading washers. I have had good luck just using a quality construction adhesive similar to PL Premium it's available at most home centers.
You could make a wood nosing to transition the edge of the counter top or you could use a pre made wood or laminate stairnose for the edge. I don't know where you purchaced the tile butI know Menards has an overlapping stairnose that works perfect for the edge. I also think Avaire is going to have a line of transition profiles available soon.
Hope this helps.