This question is heard almost daily on bike forums with different A, B and C. Here is an almost complete (by year 2012) table of what will work.
What is intentionally not listed here (for the sake of compactness):
Table cells show approximate movements of the derailer from the corresponding row, pulled by the shifter from the corresponding column. No color indicates that the movement is not suitable for any cassette. Color (backround or font) shows that this combination will work with the cassette with spacing, corresponding to this color. Backround is painted for cells, corresponding to the shifter and derailer from the same "system" (such as for example "Shimano 9 speed"). Naturally, they are designed to work together and the movement is equal or very close to the spacing. Bold font is colored for cells, which are not "designed to work together", but still shift this cassette. Italic is for same cases, but when the shifter has fewer clicks than the cassette cogs (so such combinations are in most cases not very practical).
Some earlier writings on this issue (I do not know of a complete one):