Finding shortest and longest paths between two vertices in a DAG
For the shortest path problem, if we do not care about weights, then breadth first search is a surefire way.  Otherwise Dijkstra's algorithm works as long as there are no negative edges.

For longest path, you could always do Bellman-Ford on the graph with all edge weights negated. Recall that Bellman-Ford works as long as there are no negative weight cycles, and therefore works with any weights on a DAG.