One of the most common examples of two dimensional collisions is the collision between billiard balls. Billiard balls move only on the two-dimensional surface of the billiard table (usually!). In the three videos below, a billiard ball at rest is struck by the moving cue ball coming from the left.
In Video 1, the collisions is almost grazing, with the cue ball maintaining most of its initial speed and struck cue ball moving off slowly at nearly 90 degrees.
In Video 2, the collision is almost head-on, with the billard ball moving quickly away and the cue ball moving slowly after the collision.
In Video 3, the collision is less head-on, with both the cue ball and billiard ball moving off with roughly equal speed.