Silly string is a great way to enhance any party and the games played there. If you have a clothes line you can spray the product over the lines using large, sweeping strokes of your arm. Once in place you can play a variation on limbo seeing how low you can go without hitting any strands of silly string. Another idea is to use the product in place of, or in addition to, contemporary streamers. Used alone you may hand a can to each party participant and when everyone is present and ready they have decorate the room, and each other, with the festive string.
Tag is one game easily enhanced with silly string. Simply arm whoever is "it" with a can of product and whoever they hit with the string is now "it" and able to use their own can. The Jolly Butcher Boy is another game that silly string can be incorporated into, as it too has a chasing / tagging element. In the game you have two teams who take turns doing a pantomime which the other team guesses. Once the other team guesses correctly, the acting team runs back to their established "safe zone." Any players tagged by the product are then placed onto the other team.
You can choose the winner either when you have everyone on one team, or (if you have a very large group of people) when one team has reached a predetermined minimum amount of people. For both these games silly string adds a lot, not only for its originality and the enjoyment of using it, but also because it allows you to avoid having to settle disputes from people claiming either that they tagged someone or not being tagged and claiming they were not.
For older individuals who control over their can is more proficient you could play Pictionary on an outside stretch or lawn, cement, or patio, using the product to draw your objects. This is especially fun as people tend to get wild and excited using the silly string, and you could have implemented rules for each rule, such as that you would be limited to one can per round so that if you ran out you would have to reconstruct the already drying product to make any alternative pictures.