You can get them at any level, I got my first one shortly after starting the game.
From 10km eggs you can hatch Elekid, Magby, Smoochum, Dratini, Omanyte, Kabuto, Aerodactyl, Pinsir, Hitmonchan, Hitmonlee, Lapras, Scyther and Snorlax
Prior to the baby Pokémon being introduced you could hatch Eevee, Magmar, Electabuzz and Jynx. It's possible Hitmonchan and Hitmonlee will be replaced by Tyrogue.
How many eggs have you gotten? I'm at level 24 and have gotten 162 eggs and have gotten 12 10km eggs. I hatched Scyther, 2 Eevee, Lapras, 2 Electabuzz, Magmar, Pinsir, Dratini, Elekid, Magby, Smoochum
Right now I've noticed 2km and 10km eggs are a lot more uncommon, I get 1 or 2 of either 2km or 10km for every 10 5km eggs I get, they say they have even spawnrates but I doubt it. I also don't believe it's based on location as in the past 2km eggs were as common as 5km eggs.