Views PHP Filter is a powerful way to customize your Views result set -- but it can be a little difficult to jump into at first. Users have generously donated the following examples so that others can get a general idea of how it works and figure out how to adapt the filter for their purposes. Feel free to throw in more examples by creating a child page -- the more the merrier!
The "official" text on how Views PHP Filter works, from its README:
A new filter, labeled "Node: Node ID", will appear as addablein your Views filter lists. If you add that filter, you'll note the "Options" dropdown will have two choices: "PHP code" and "ID list". "PHP code" will take a snippet of PHP as its value (without the <?php and ?> bracket tags), which should return an array of integers representing node IDs. The filter will evaluate the PHP, and filter on the numbers in the return array. "ID list" will simply take a list of numbers, separated by commas, and filter those node IDs. This is currently used mainly for testing, but may survive to release if someone finds it useful.
(The node ID list functionality did survive, it turns out.) Too confusing? Check out the following examples to get a better idea.