This post was inspired by the simple functions discussion on Bill's post and this question on unique paths.
A path is just a way from getting from point A to point B. A simple path is a path that doesn't cross itself. Some people use "path" to mean simple path and "walk" to mean a general path (like in random walk) but lets not quibble on notation.
To find a path you just keep going until you get there. To follow a simple path you need bread crumbs, some way of remembering where you've been. Often it doesn't matter. There is a path from A to B if and only if there is a simple path. The shortest path from A to B on a graph of positive edge weights is always simple. Ah but it isn't always so simple.
The randomized and deterministic log-space algorithms for undirected connectivity don't give anything close to a simple path. Counting the number of paths is easy, just take powers of the adjacency matrix. Counting the number of simple paths is #P-complete. The longest path is either infinite or easy to find. The longest simple path (Hamiltonian path) is NP-complete. Playing Go with players requiring to follow a simple path (no repeating a board position) is EXP-complete despite being played on a poly-size board. Making paths simple make them much more complex.
In our lives we need the ability to go back, to learn from our mistakes and try other possibilities. There is no where you can go without following a simple path but to follow one requires omniscience and trying to stay on a simple path will limit your choices. Life is not a simple path.