Web services to mine the social web?
Tweepy is one of the best libraries for analyzing and hacking around with the Twitter API.  (Being a contributor for tweepy, I can vouch for it's stability and quality)

For a Python wrapper for the Facebook graph API, you can use the Facebook-Insights library, which is well-maintained and neat documentation.

There are services out there which can mine you information, but they are limited to the complexity of the query.

For example: "How many people tweeted about banana on Monday?" can be answered from existing tools

"How many people happy people tweeted about banana on Monday" can also be done, but would require more efforts and the software or tool should be able to detect emotion.

So, if you are into research, I would advise you to go with the API's and good ol' programming!