This is from Harta's blog here Some of the links were broken, so I wanted to update the ones which are still available.

Dynamic Programming (DP) :

Classic Dynamic Programming

I. Longest Common Subsequence (LCS)

1. SAMER08D

II. Longest Increasing Subsequence (LIS)

1. Beautiful People
2. MDOLLS
3. MSTICK
4. MCARDS

III. Edit Distance

IV. Matrix Chain Multiplication

1. Mixtures

V. Knapsack

1. Scubadiv

Advanced DP

I. DP k-th lexicographical string

1. z-01 paths
2. z-board
3. Linear Garden (IOI 2008)

II. DP tree

1. z-sumpaths
2. River (IOI 2005)
3. z-company
4. Greedy Hydra (CNOI 2002)
5. VOCV
6. PT07F
7. PT07X
8. nagibni

III. DP+ BIT/segment tree

1. Salesman (IOI 2009)
2. explosion
3. intervali
4. RENT
5. INCSEQ
6. INCDSEQ

IV. DP+ convex hull

1. Batch Scheduling (IOI 2002)
2. NKLEAVES
3. Harbingers (CEOI 2009)
4. Commando (APIO 2010)

V. DP pre-processing

1. Oil (APIO 2009)
2. Garden (IOI 2005)
3. Pyramid (IOI 2006)

VI. DP bitmask

1. Reklame
2. Chess
3. Bond
4. TRSTAGE
5. HIST2
6. LAZYCOWS

VII.

1. Grid (BOI 2008)

VIII. DP matrix multiplication/ DP using recurrence

1. SEQ
2. SPP
3. z-funkcija
4. mit-indiv09-words
5. Reading (Balkan 2009)
6. Super Climber
7. z-mario

IX. DP+ trie

1. MORSE

X. DP+geometry

1. MPOLY
2. CVXPOLY
3. MTRIAREA

XI. DP + Binary Search

1. Game (IOI 2008, Practice session)

XII. DP + Knuth Optimization

1. Breaking Strings

Other Problems in SPOJ can be found here by pt1989 Thanks to pt1989

Here are problems in acm.sgu.ru 269 273 304 317 356 396 445 447 458 489 494 Thanks to natalia

Problems tagged as DP in SPOJ can be found here

Reference:

1. Topcoder
2. Codechef

Special Thanks to Harta for the Original Blog