Unlike the very similar Phenylalanine, Tyrosine contains a reactive hydroxyl group, thus making it much more likely to be involved in interactions with non protein atoms.
Like other aromatic amino acids, Tyrosine can be involved in interactions with non-protein ligands that themselves contain aromatic groups via stacking interactions.
Like other aromatic amino acids, Tryptophan can be involved in interactions with non-protein ligands that themselves contain aromatic groups via stacking interactions. Tryptophan and other aromatic amino acids can be involved in binding to poly-proline containing peptides, for example, in SH3 or WW domains.
A common role for Tyrosines (and Serines and Threonines) within intracellular proteins is phosphorylation. Protein kinases frequently attach phosphates to Tyrosines in order to fascilitate the signal transduction process. Note that in this context, Tyrosine will rarely substitute for Serine or Threonine, since the enzymes that catalyse the reactions (i.e. the protein kinases) are highly specific (i.e. Tyrosine kinases generally do not work on Serines/Threonines and vice versa).