Tactile sensors measure force applied to them. This can be in an on-off fashion or as a more or less accurate measurement.
Simple Contact Sensor 
Bumper switches 
One of the most simple sensors available are contact sensors or bumper switches. These sensors use some form of bumper to press a button when the robot comes in contact with another object. A well built bumper switch is a very reliable sensor, but since these detect by touch, they're not very practical on fast or heavy robots.
One key point on bumper switches (or any kind of mechanical switches) is that they don't give a clean signal when closed. The contact tends to "bounce" a bit.
Whiskers use the same principle as bumper switches, however they give a slightly larger detection range and so avoid the need to bump against other objects. One common design is to mount the whisker through a circular bend wire. When something hits the whisker, it bends and touches the circular bend wire. The electrical contact formed in this way is used to detect the object.