First, let's just get the basics of what an egg move is:
An Egg move is any move passed down from a Pokémon breeding pair to their offspring, which it would not normally possess at the level it hatches. The term is also frequently used specifically for moves that a Pokémon can acquire only from breeding (i.e. moves that the offspring cannot learn via level-up, TM or HM, or Move Tutor), though a Pokémon can inherit moves from its parents in other ways.
Before breeding a Pokémon, one must consider whether to use any Egg moves in that Pokémon's moveset, and breed accordingly. Sometimes, to get a certain combination of moves onto a Pokémon (such as a Spinda with both Wish and Baton Pass) several steps must be taken; this is called chain breeding.
Prior to Generation VI, all methods of learning Egg moves required the father to know the move prior to breeding, which made certain combinations of moves impossible to possess: e.g. Tentacruel can learn both Rapid Spin and Mirror Coat as Egg moves, but no Pokémon in the Water 3 Egg Group can possess both moves at the same time. (Such a combination is possible in Generation VI, if one parent knows Rapid Spin and the other knows Mirror Coat).
So now lets get right into it.
Fully Evolved Pokemon
Fully evolved Pokemon or even mid-stage Pokemon won't have egg moves, although there are quite a few exceptions to this. For example: Magmar, Electabuzz, Snorlax, and pretty much almost any Pokemon that recieved a pre-evolution in the form of baby Pokemon will have egg moves(minus Wobbuffet and Jynx). Other Pokemon such as Carnavine and Druddigon who do not evolve from or into other Pokemon also have egg moves, since when hatched from an egg, they are already a fully evolved Pokemon.
Nearly all baby Pokemon were introduced in generation 4 (exceptions are Smoochum, Elekid, and Magby) along with new evolutions for previous gen Pokemon (i.e. Magmar's evolution chain)
Like their evolutions, baby Pokemon may also hatch with egg moves. Take for example Chansey and Happiny. When breeding Chansey or Blissey, you will usually end up with a Chansey egg. If you make Blissey/Chansey hold a Luck Incense, you will end up with a Happiny egg. So what does all this mean anyway? Well, since both Chansey and Happiny can hatch from an egg, the both will be able to learn Egg Moves (such as Seismic Toss.)
There are some Pokemon that when hatched from an egg, they will not hatch knowing egg moves. These Pokemon are as follows (and the answer to your question):
-Ditto (as you cannot breed Ditto for a Ditto egg)
-All legendary Pokemon
Well, that was a lot of typing ^^' Hope this helps :)