In an UML component diagram, how does one tag or identify a component as a database, so that it's easily recognizable? In the old days there was the cylinder symbol for showing database but that's not part of the UML. Same goes for an application server for instance, how would that be shown?
Are stereotypes applicable here? Can the component symbol be enhanced with graphical elements?
You tag databases <<database>> and servers as (it appears) <<infrastructure>> according to Scott Ambler. I pulled this information from Figure 1, but I would recommend reading this article (and his other articles - they are good reads).
Something else I want to point out - UML is just one method of modeling. In formal documentation, I try to adhere to the standard. However, when planning and documenting for the team, I use whatever makes sense and is understood by the team. For you, that might mean putting a cylinder labeled "DB" or the name of the DB in the component box.
Just use the <<database>> for the component diagram.
For a more detailed information check out this article: http://www.sparxsystems.com.au/resources/uml_datamodel.html
UML can be extended through profiles.
The key extensibility mechanisms are sterotypes, constraints, and tagged values.
Sterotypes can have an optional stereotype icon.