Wobble Hypothesis

61 possible codons - 20 amino acids - all due to the degeneracy of code as given in the wobble hypothesis.

Under the Wobble Hypothesis, the third position in a codon can tolerate some mismatch. Thus a single type of tRNA can recognize more than one codon.
Example: a tRNA with anticodon sequence of 3'-AAG-5' can recognize a 5'-UUC-3' and a 5'-UUU-3' codon even though only the former is perfect match according to the AU/GC rule.

The ability of a single tRNA to recognise more than one codon makes it unnecessary for the cell to make 61 different tRNA molecules for 61 different codons.

It probably also provide some leeway for mutations? =)