I have two neighbors that were in LDRs. They now have happy, stable marriages. I actually know quite a few people who had happy endings with their LDR.
With that said, like everyone else (local or otherwise), they had previous failed relationships. It works out with patience, commitment, and effort when two people are right for each other. The physical stuff may not be there right away or full time, but if your relationship revolves around sex, it probably isn't going to be lasting anyway.