There's a few algorithms we have for sorting data, finding the maximum and minimum, finding the shortest path between nodes etc.
I've started looking into the qualitative analysis of user-generated data and have come across latent semantic anaylsis. What other techniques exists for the analysis of textual data ... and possibly other media?
That's...a pretty broad question. Analysis of user-generated data, textual or otherwise, is typically done through specialized applications of general data mining techniques. If you're interested in learning more about this extremely wide field, I'd start with that wikipedia link, follow all its references, then hit Google Scholar. By then you should know what sorts of techniques you're interested in.
If you have a specific problem in mind, post about it; there's a community of AI guys here on SO and one of us can probably suggest an approach, or at least a more focused line of research.