Fixed action patterns are invariant animal "actions" that occur in response to specific stimuli. The key difference from normal animal behavior appears to be that these actions are fixed (think FSAs), bypassing learning and feedback that other actions have. According to , "once a fixed action pattern is triggered, the behavior continues until completion even in the presence of other stimuli or if the behavior is inappropriate."
Greylag Goose: Seeing an egg out of the nest triggers an action to roll the egg back into the nest. I found an old video of this and uploaded it to youtube: http://www.youtube.com/watch?v=vUNZv-ByPkU
Digger Wasp: The FAP the wasp uses is (from ):
- Fixed-Action Pattern: she places the cricket 2.5 cm from the nest
- Sign stimulus: Nest site
- Fixed-Action Pattern: She enters the nest and inspects it.
- Sign stimulus: Presence of cricket 2.5 cm from nest
- Fixed action pattern: She exits the nest and retrieves the cricket
- Sign stimulus: Presence of cricket 2.5 cm from the nest
The interesting part of the FAP is that if the cricket is moved during the next inspection stage, the wasp will retrieve the cricket and repeat the FAP from the first step. She cannot get past the inspect the nest step if the cricket is not where she left it when she tries to retrieve it.
This is explained very well in this video by Richard Dawkins: http://www.youtube.com/watch?v=qm-0Z0ceezQ#t=2m30s
Here is a video showing a real digger wasp: http://www.youtube.com/watch?v=5t2p4ukzL74
The wikipedia page on digger wasps (genus Sphex) is especially interesting; I've pasted it here, verbatim from 
Some Sphex wasps drop a paralyzed insect near the opening of the nest. Before taking provisions into the nest, the Sphex first inspects the nest, leaving the prey outside. During the wasp's inspection of the nest an experimenter can move the prey a few inches away from the opening of the nest. When the Sphex emerges from the nest ready to drag in the prey, it finds the prey missing. The Sphex quickly locates the moved prey, but now its behavioral "program" has been reset. After dragging the prey back to the opening of the nest, once again the Sphex is compelled to inspect the nest, so the prey is again dropped and left outside during another stereotypical inspection of the nest. This iteration can be repeated again and again, with the Sphex never seeming to notice what is going on, never able to escape from its programmed sequence of behaviors. Dennett's argument quotes an account of Sphex behavior from Wooldridge's Machinery of the Brain (1963). Douglas Hofstadter and Daniel Dennett have used this mechanistic behavior as an example of how seemingly thoughtful behavior can actually be quite mindless, the opposite of free will (or, as Hofstadter described it, antisphexishness).
In addition to this seemingly instinctive and programmed behavior, the Sphex has been shown, as in some Jean Henri Fabre studies, not to count how many crickets it collects for its nest. Although the wasp instinctively searches for four crickets, it cannot take into account a lost cricket, whether the cricket has been lost to ants or flies or simply been misplaced. Sphex drags its cricket prey towards its burrow by the antennae; if the antennae of the cricket are cut off, the wasp would not think to continue to pull its prey by a leg.