String Problems Link :-
1.) http://www.spoj.com/problems/VPALIN/
2.) http://www.spoj.com/problems/ANARC08C/
3.) http://community.topcoder.com/stat?c=problem_statement&pm=11714&rd=14551
4.) http://www.codechef.com/problems/PTOSS (see once)
5.) http://community.topcoder.com/stat?c=problem_statement&pm=6017 (Aho-Corasick)

Reference :- http://www.quora.com/Competitive-Programming/What-are-some-good-problems-that-uses-Knuth-Morris-Pratt-Algorithm-on-TopCoder-Codeforces-CodeChef-and-SPOJ