The Asgard hail from a distant Ida Galaxy. The are the most advanced race known to man, with the exception of the ascended Ancients. The Asgard are, by their own statement "friends of all and protectors of all, except the Goa'uld, with whom they are at war". Long ago they came to Earth where they gave rise to Norse mythology. They have protected many races from the Goa'uld, but their recent conflict with the Replicator has force them to take a more passive role in the Milky way.
The Asgard evolved on the planet Othala in the Ida galaxy. They were contemporaries of the Ancients, who at that time held a wast empire in the Milky way. Along with the Furlings and the Nox, these races formed the Alliance of Four Great Races, a group of the most advanced races knwon in the universe. With the Ancients forced to ascend due to their plague, the Asgard took care of the fledgling Humanity, viewing them as children of the Ancients. This brought them into conflict with the Goa'uld, who have also discovered humanity, and decided that they would make excellent hosts and slaves for them. The Asgard, not troubled by the Goa'uld's scavenging if ancient technology and enslavement of younger species, went to war with them, and were easily able to dominate them with their superior ships and technology.
However, the Asgard were forced to pull out of the conflict when they discovered in their own galaxy a machine menace known as the Replicators. Not wanting to leave humanity to the will of the Goa'uld, they forced the Goa'uld system lords to sign a treaty, preventing them from attacking a number of protected planets, on which humans are free to develop. On those planet, the Asgard took the guise of Norse Gods in order influence the humans.
The modern humans from Earth (given the name Tau'ri, the first ones, by the Goa'uld slaves), made contact with the Asgard in 1999, when Colonel Jack O'Neill had a repository of ancient knowledge downloaded into his brain. With it he dialed out to Othala, where the Asgard removed the knowledge, saving his life. From that point on the Asgard, led by Supreme Comander Thor, were the most powerful allies of the Tau'ri, even though their war with the replicators prevented them from taking action many times.
In 2000, Asgard enlisted Earth into their protected planets treaty, forcing the denying it to the system lords, which is probably the only reason the Earth is still around. However, in the same year, Asgard unwittingly endangered Tau'ri when one of their ships was infested by the replicators, and set its course towards the Earth. However, the primitive weapons of the Tau'ri proved to surprisingly effective against the replicators, which always strived to upgrade themselves with more sophisticated technology. Realizing this, The Asgard ask their help in stoping a replicator attack on their home planet of Othala. With Major Samantha Carter's help they were able to destroy the replicator ships and return to earth in time to Save Jack O'Neill and Tealc from being killed by the replicators left on Earth.
The war with the Replicator, however, raged on throughout the galaxy. In 2003, Asgard used the android Reese,the "mother" of the replicator, first discovered by SG-1, to lure all the replicators to their colony of Hala, and there trapped them in a time dilation field, destroying their own homeworld in the process. Having lost their homeworld, the Asgard settle on their colony of Orilla, making it their new homeworld.
The replicators escape the following year and attack the Asgard homeworld. The Asgard intercept the Replicator ship with six O'Neill class battlecruisers and obliterate it, but they cannot prevent thousands of Replicator blocks from falling on Orilla. However, with Jack O'Neill having previously once again downloaded the repositroy of knowledge into his mind, they are ale to use Ancient knowledge to devise a weapon against which the replicators are powerless. With this anti-replicator gun they are able to render all replicators on Orilla inert, and finally turn the tide in the war.
The Replicators would later invade the Milky Way Galaxy and destroy the Goa'uld system lords, only to be destroyed themselves when the Tau'ri use the stargate network to aply the Anti-replicator gun on a galactic scale. the Asgard later replicated this feat in their own galaxy, destroying the replicators for good.
For helping them defeat the replicators, the Asgard agreed to upgrade the Tau'ri fleet of ships, making them the most powerful faction in the Milky Way, a fact which would come in handy to them when the Ori invaded the Milky May.
During the Ori Invasion, the Asgard send several ships to aid the allied Milky way fleets, but were generally uninvolved in the war, this was eventually revealed to be because their tampering with their own genetic structure gave them an incurable disease which would destroy them soon. Rather than simply await death, the Asgard Gave all their knowledge to the Tau'ri, proclaiming them to be ready to take their place in the alliance of Great Races. They then committed a mass suicide, destroying their planet and three Ori cruisers with them.
A renegade faction of Asgard survived in Pegasus, however. These Asgard splintered from the others 10,000 years ago over their belief that they should experiment on humans to solve their cloning problems. They traveled to the Pegasus galaxy and continued their experiments, but were forced into hiding after the Wraith defeated the Ancients. When their planet becomes too toxic for them, they tried to use the Attero Device to destroy the Wraith, but were stopped by the Atlantis expedition.
The Asgard have a striking resemblance to the Roswell Greys, and may have in fact inspired the tales about them in the first place. They have an advanced cloning system, allowing them to transfer their minds into a clone body whenever their original one is destroyed, making them effectively immortal. However, it was revealed that this cloning process is not prefect, and with thousands of years cloning they have degenerated from relatively humanoid forms, to the forms they have now. While trying to solve this problem, they unwittingly created a defect which accelerated their degeneration, leading to their mass suicide.
Asgard are governed by a body called the Asgard high council, which consists of seven members, among which are Thor and Freyr. They masquerade themselves as Norse Gods to people who they protect, in order to ease the level of development gap. To find out when a race has advanced enough to see them in their true form, they leave behind tests, which are generally mathematical in nature for them to solve.
The technology of the Asgard is nearly on par with that of the Ancients. With it they are easily able to dominate such lesser race like the Goa'uld, who in fact greatly fear the Asgard. Their most
recognizable technology is their transporter beam, which has no need for a platform on either end, making it a wast improvement over that of the Ancients and the Goa'uld.
Also notable are their hypredrives. Asgard possess the fastest ships in the Stargate universe, which are capable of crossing inter-galactic distance in a matter of minutes. Their Plasma beam weapons have also shown to have no equal among even the Ancient ships.
As mentioned before, they are quite skilled in cloning.