In the main series games there are only two types of Pokémon eggs, this being Normal Eggs and the Manaphy Egg.
Normal Eggs are ordinary Eggs that are produced when two compatible Pokémon breed.
"The Manaphy Egg is an event item which can allow for the player to receive the Legendary Pokémon Manaphy. First received through a special code in Pokémon Ranger, the player could transfer it to the first Generation IV game and hatch it."
Here is an image of a Normal Egg and the Manaphy Egg in Generation V:
In the Pokémon Anime, Pokémon Eggs each have different designs. Each egg usually has same design as the Pokémon that hatches from it, with the exception of Elekid and Magby who are the only Eggs whose designs depict those of the Pokémon's evolved form, rather than the Pokémon it directly hatches into.
Here are some images of Pokémon Eggs in the Anime:
In other Pokémon Games:
In Pokémon Snap there's Eggs of the Legendary Birds; Articuno, Zapdos and Moltres.
Articuno: This Egg is in the Cave area. It is silver and has a crystalline form. It hatches with the aid of two dancing Jynx.
Zapdos: This Egg is in the Tunnel area. It is yellow with a jagged electric pattern on it. It hatches with the aid of a Pikachu's Thunderbolt.
Moltres: This Egg is in the Volcano area. It is white with a red flame design on it. It hatches when a Pester Ball or an apple knocks it into the lava.
While some Pokémon hatch from plain white Eggs in Pokemon Channel, a number of Eggs that have appeared in the anime are a main feature on the channel. Pokémon with Eggs seen include Bellsprout, Hoppip, Igglybuff, Ledyba, Mudkip, Oddish, Phanpy, Smoochum, Swinub, Teddiursa, Torchic, Treecko, Wooper, and Zubat.
Here is what an Egg looks like on Pokemon Stadium 2:
(More to be added)
Hope I helped :)