BalusC excellent answer covers most of the patterns for web applications.
Some application may require Chain-of-responsibility_pattern
In object-oriented design, the chain-of-responsibility pattern is a design pattern consisting of a source of command objects and a series of processing objects. Each processing object contains logic that defines the types of command objects that it can handle; the rest are passed to the next processing object in the chain.
Use case to use this pattern:
When handler to process a request(command) is unknown and this request can be sent to multiple objects. Generally you set successor to object. If current object can't handle the request or process the request partially and forward the same request to successor object.
Useful SE questions/articles:
Why would I ever use a Chain of Responsibility over a Decorator?
Common usages for chain of responsibility?
chain-of-responsibility-pattern from oodesign
chain_of_responsibility from sourcemaking
