Finding a massage any time of the day or night might be difficult in rural areas, but in most metropolitan areas Yelp and Craigslist are places to find 24-hour massage services. Massage Anywhere has both search and listing services for those needing and those providing massages nationwide.
Many hotels also offer massage services and many resorts have massage staff or massage specialists nearby. The concierge is a good place to start if you are in need of a massage in an unfamiliar locale. Sites that allow services offered listings specific to an area, like Craigslist's therapeutic services section, are good sources for finding a masseuse.