These programs all use SRTM (Shuttle Radar Topography Mission) data which is available on 30 meter (approx. 100 ft.) intervals for the United States. I don't know the accuracy of the data and in some geographic areas the data has been augmented from other sources, but 100 ft. spacing (if used by the mapping program) will capture a fair amount of subtlety in the elevation profile. I don't use Mapmyride much, but the standard elevation plot doesn't represent itself as high fidelity. Ridewithgps allows you to expand the elevation profile and it looks like the data is near 100 ft. geo resolution, but I do take this mapping programs max. grade with a grain of salt due to data errors.
Average grade at 1/2-1 mile intervals is useful because these approach steady state efforts on our tandem; I like to see these grades <10%. Grades over shorter intervals can somewhat be estimated with a mapping program, but the best source is probably someone who's been there done that.