I tend to use the mapping software on the logging site RunPartner.com, I find this to be more accurate than mapmyrun. Also, RunPartner isn't infested with ads like mapmyrun is, probably the main reason I prefer it, along with the fact at Runpartner the mapping is integrated onto the same site where I log. The RunPartner mapping also has the same nice features as mapmyrun, such as 'autorouting' that when enabled will connect two points assuming you followed the roads, which makes mapping much faster and more convenient.
Still, of course, it is not *perfectly* accurate, and neither is a GPS.
The main reason runs mapped online (both mapmyrun and RunPartner) tend to be a little long, is because you don't actually run in the middle of the street and make 90 degree turns, etc. If you are able to very carefully make it follow your exact route, then yes it will be exactly right, but who has time for that? Better just to keep in mind that the mapped distance is actually about .1 miles further than you ran (for a 5 mile run on mapmyrun or a 10 mile run on RunPartner). Another detail, the more corners there are on the run, the more the mapped distance will be an overestimate (unless, again, you are going through and 'fixing' all of the corners, each of which adds like 5-15 meters).