I can't agree with Clinton and Raedwulf. The traditional drinking games of old performed at German universities are mostly connected with songs to enforce and enjoy hard drinking. There is a great variety of performances, e.g. where to put the glass when singing or when to drink, or where to drink (under the table, upon the table &c).

The Four Task Card Deck Song

You need:
1 deck of 32 cards
1 glass, pint

(The deck of 32 cards contains the numbers referred to below)
Put a full glass in the middle and sing:
And the seven and the eight and and the nine and the ten,
and the knave and the queen and the king and the ace
Deal out a card at every number sung, one for each participant.
If the card dealt corresponds to the number sung, the person in question has to perform the task which is due in the series.
Task One: Take the first gulp.
Task Two: Drink until a part of the bottom is seen.
Task Three: Drink the rest.
Task Four: Pay the next glass.
Repeat ad nauseam or until the majority cries for mercy.

You will see that after some repetitions the hardest task will be Task Two since Task One will be performed with the smallest quantity possible, and everybody will be eager to perform Task Four only.

A game without singing is
The Beer Clock

You need:
1 hammer
1 nail
1 cord, length 1'
1 piece of chalk
1 key
1 glass, pint, for everyone

Hammer the nail vertically into the table. Draw a circle around the nail with the cord and the chalk. Divide the circle into as many equal sections as there are participants. Put the key with its hole over the nail.
Snip the key with your fingers to set it into rotations not less than 2 rounds. Where the key stops mark the section.
Repeat this ritual until one participant has three marks (bad luck). He will stand you the next round.
The game may be repeated ad nauseam or until the majority cries for mercy.

Cheerio
Wilfried