I would like to be somewhat good at string searching and pattern matching, could you point me to some good online resources? Exercise problems would be great. Thanks.
Are you already familiar with the main algorithms in the area? Are you familiar with this site a huge and well-maintained list of references in pattern matching?
I don't see how one could come up with a list of exercised for string matching, except "implement all main approaches and test them on a lot of data". And data is really easy to come by: you can grab any text file and it will do (you can create a positive example by seeking to a random location in the text file and getting n characters, and for a negative example any random string will do).
There is a huge literature in the area, of course, and the first link I posted can steer you in that direction.