On a printed circuit board, I see lots of tiny letters and numbers. Is there some kind of standard that dictates what letter indicates what type of component?
The technical term for the markings is "reference designators" (aka "refdes") and there are a few standards can define them. Take a look at this wikipedia page for a quick overview.
http://en.wikipedia.org/wiki/Electronic_symbol

http://blogs.mentor.com/tom-hausherr/blog/tag/reference-designator/



For schematic components, most EDA tools start off with one or few alphabets and then a sequential number. For example, R1 for the first resistor, C1 for the first capacitor, IC1 for the first IC and so on. You can download a free EDA tool such as Eagle to play around. Also, see the wikipedia page for a few more examples.

For PCB footprints, different vendors do make naming convention suggestions. See Altium's suggestions here, for example.

Edit: I do NOT know anyone personally that refers to this as a strict standard or a standard at all. It's mostly what you are used to and familiar with.
