This happened when i was around lv 10 playing an altermer pure mage with my companion lydia. It started with my first vist to winterhold. I was strolling down the street blasting my newly acquired shouts into the air when suddenly i heard a roar. I looked around and saw a dragon flying around a mountain in the distance. it scared the crap out of the people but it eventually flew away and i continued on my journey to the college thinking nothing of it.
After passing the entrance test i quickly attended finished the first mission. after telling the arch mage about the discover i made i walked out side. Once again i heard a roar, louder this time. and i looked up to see a dragon approaching. it landed on the courtyard wall and presumed to spit a torrent of fire upon us. it caught me off guard but I quickly summoned a flame atronarch and put up a ward to deflect the fire. after defeating lydia it landed on the courtyard and continued to breath fire at me so i hid behind a pillar while i waited for my magicka to recharge, blasting firebolts every few seconds. after it had finally been defeated all the students and teachers of the college of winterhold came out of there respective rooms and continued on there merry way completely ignoring the dragon skeleton in the middle of the courtyard. At this point my jaw hit the floor they had all been there watching and didn't lift a finger to help and then after wards they pretended like it didn't happen. I sighed and left. upon my return the dragon skeleton had vanished! i can only guess what the colleges is now doing with it.

My first random dragon encounter was with two dragons at the same time. I know Todd said this was possible, I just didn't expect it for my first encounter.