I would have to qualify my answer by saying that first it will be country specific(US in my case)- and possibly even region specific (midwest/ozarkian); and second it attempts to include a few tunes from each of the three primary fiddle tune keys - D, A and G. We dont do much fiddle work in the key of C at the basic level here. Finally I am making the assumption that you are looking for tunes to teach a beginning fiddler or at least someone new to the genre.   These are all tunes that any experienced fiddler in these parts would have to know (and would probably be sick and tired of).

With that in mind, our little school here teaches a number of tunes in its lower level fiddle classes - among which the most repeated seem to be, albeit in no particular order other than key:

Key of D
Fly Around My Pretty Little Miss (Hop High Ladies, Susannah Girl etc)
Angeline the Baker (or Angelina Baker)
Eighth of January (Battle of New Orleans)
Robinson County
Soldiers Joy

Key of G
Chase the Banshee (we have Banshees in Missouri)
Miss McLeod's Reel (Did you ever see the Devil Uncle Joe?)
Red Wing
Seneca Square Dance
Going Down To Cairo (Good Bye Liza Jane)

Key of A
Old Joe Clark
Cripple Creek
Horse and Buggy
Greasy Coat (got to have some of the modal tunes in there)
Cluck Old Hen (ditto)

That's 15 not 10. Those arent my necessarily personal favorites and I am not a fiddle player, but they seem to be the ones that are most used for basic teaching here so I assume they are good for that purpose.   If we were to have our young fiddlers put together a program for a 3 hour square/contra dance, most if not all of those tunes would be on the list. We probably teach simple versions of some of these tunes - so I am assuming these are tunes which either have a simple base melody to start with or seem to permit simplification of a more complicated base melody without losing too much. Obviously good players play all of these tunes in a manner that would be over the head of a learner.

I have not included any waltzes - while we play them and teach them here, I don't treat them as being "fiddle tunes" as we normally use that term here, but some good ones have been mentioned in the thread above. Of course if you're really dealing with total beginners, the Old Town School in Chicago teaches everyone Go Tell Auint Rhodie the first day, but I dont consider that a fiddle tune either.