Just limiting the discussion to electric arc processes there are- SMAW (stick), GMAW (mig), GTAW (tig) and others less often seen. Then there are positions- flat, horizontal, vertical, and overhead. Types of joints... . Materials... . So depending on what you consider to be different there are thousands of different welds. They are used for everything from wiring the pins to the silicon in an integrated circuit (tiny gold wire welded on by laser) to construction of oil tankers. What I'm driving at in my rather wordy way is that you need to ask a more specific question.
http://www.machinist.org/army_welding/
Try browsing here (the army welding manual). Stay interested and do come back with more questions.
Bill

All welds fit into 2 catagories...
Fillet Welds or
Groove Welds (there are lots of different groove weld joint configurations)
John Wright