Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. More info(wikipedia)
Following are some popular dynamic programming problems,
Longest Common Subsequence Problem
Shortest Common Supersequence Problem
Longest Increasing Subsequence Problem
The Levenshtein distance (Edit distance) Problem
Matrix Chain Multiplication Problem
0–1 Knapsack Problem
Partition Problem
Rod Cutting Problem
Coin change-making problem
Word Break Problem