Is there an algorithm to find all the shortest paths between two nodes?

Given a directed graph, Dijkstra or Bellman-Ford can tell you the shortest path between two nodes.

What if there are two (or n) paths that are shortest, is there an algorithm that will tell you all such paths?

Edit:

I have just thought up a possible solution. Could you just do a Bellman-Ford but when relaxing edges, if (distance[u] + w == distance[v]) then add u to the set of predecessors of v? Does this work?

For the $k$ shortest paths, there are algorithms; see for instance here.

Enumerating all shortest paths is, however, an inherently costly thing; there may be superexponentially many such paths.

StackExchange Computer Science Q#38000, answer score: 4