Overlapping subproblems solved once and reused.
Count the ways to climb n stairs taking 1 or 2 steps at a time.
Max loot without robbing two adjacent houses — the classic take-or-skip DP.
Fewest coins to make an amount — bottom-up DP, not greedy.
Can a string be split into dictionary words? Reachability DP over prefixes.
Longest strictly increasing subsequence — dp[i] = best run ending at i.