Digimon have six stages, as they Digivolve they go to the next stage getting stronger than the last one. All Digimon start out as an egg. When digimon die their leftover data reforms into an egg, which may or may not retain its previous memories depending on how much data was left.
Fresh (Baby I) Digimon
This is the form every Digimon takes after they hatch from an egg. Baby Digimon are weak and only know a single attack. That attack is the baby shooting bubbles form its mouth. The Baby Digimon digivolves to be In-Training Digimon
In-Training (Baby II) Digimon
In-Training Digimon digivolve from Baby Digimon. They're a little stronger, but they can only perform the same move as Baby Digimon. Then In-Training digivolves to become Rookie Digimon.
Rookie (Child) Digimon
Rookie Digimon Digivolve from In-Training and Digivolve to Champions. Now the Digimon can learn many different techniques, and for the most part grow limbs. In the anime, this is the most common form for a Digimon to be seen in, and higher leveled Digimon often revert back to this form when they are done fighting.
Champion (Adult) Digimon
Champion Digimon Digivolve from Rookie and become Ultimates. This when Digimon have a huge jump in power.
Ultimate (Perfect) Digimon
Ultimate Digimon was the final stage for a good portion of Season one. They Digivolve from Champions and can Digivolve to Mega Digimon, which were introduced midway through the first season.
Mega (Ultimate) Digimon
The highest level introduced midway through the first season of the anime. Despite being the highest level of Digimon some Megas can Digivolve into other Megas.
Artificial Digivolutionary Stages
There are other Digivolutionary stages that Digimon may have, but in the card game are equated to one of those listed above.
Debuting in Digimon Adventure 02, Armor Digimon are equated to Champions in the card game and most video games, and Ultimates in the Digimon Story games. Digimon can reach this stage using a Digi-Egg (though a different kind than Digimon are born from). There are 9 Armor Digi-Eggs (Courage, Friendship, Love, Sincerity, Knowledge, Reliability, Hope, Light and Kindness), as well as 2 Golden Digi-Eggs (Miracles and Fate).
Debuting in Digimon Frontier, Hybrid Digimon are Digimon that humans and Digimon alike can access through use of the Legendary Spirits. There are 10 elements of spirits (Flame, Light, Lightning, Wind, Ice, Water, Steel, Earth, Wood and Darkness), each with human and beast varieties. Human Hybrids are equivalent to Champion Digimon, Beast Hybrids are equivalent to Ultimate Digimon. When two spirits belonging to the same element are used at the same time a Fusion Hybrid is formed and on the same level as Mega Digimon. When five pairs of spirits are used at the same time a Unified Hybrid is born.
There are many Digimon that have no level. The majority of these Digimon were introduced in Digimon Fusion, which abandons the classic Digivolutionary stages in favor of having Digimon fuse together to create new, stronger Digimon.
Vaccine: Usually attributed to heroic Digimon.
Data: Can be attributed to good and evil Digimon alike.
Virus: Usually attributed to evil Digimon, though some virus-types like Wormmon and Guilmon are heroic in the anime.
Some Digimon don't have an attribute, a noticable exception is Calumon.