TECHNOLOGY OF THE ASGARD
Teal'c: The destruction of the hammer device in order to save my life may have caused this. If so, I am responsible.
Jack: General, I gave the order.
Daniel: I fired the staff at the machine.
Sam: And I was...there.
- Stargate SG-1, "Thor's Chariot"
-- Runic computer consoles --

The Asgard use a type of Nordic rune script on their very advanced computer consoles. They also have glowing stone-like appliances that are used to manipulate the computer consoles (as shown above).
-- Interstellar space travel --

The Asgard are a space-faring race. They are able to build powerful ships that are capable of travel and military power, the likes of which rivals even the Goa'uld. The picture above is of Thor's ship, also called Thor's chariot, and in this instance it is speedily dispatching three Goa'uld ships and a host of jaffa troops.
The Asgard's mightiest ship to date was named after their favorite Earth human, Jack O'Neill of SG-1. It did not survive for long, but had great capabilities. The trouble with their advanced ships is that they are so heavily advanced - and therefore meaty targets for the Replicators, a mechanoid race that makes new technologies part of itself.
-- Holograms --

The Asgard are capable of broadcasting different kinds of holograms. The above picture is of one type of hologram, made to look like a human man and to deliver a pre-recorded message. The hologram apparently was controlled by sensors in the room, probably centered in the stone plinth behind the hologram. The Asgard used this hologram because they did not feel the human inhabitants of the planet would be ready to accept the true, alien form of the Asgard race, but they did want to be contacted when the humans were advanced enough to figure out how. The Asgard are also perfectly capable of creating live holograms of themselves in their true form, however.
-- Teleporting - Thor's Hammer --
The Asgard are able to teleport beings onto and off of their ships. They are also able to teleport people to different locations on the same planet.

Thor's Hammer (pictured above) is a specific type of Asgard teleport device. First, the device is able to detect a Goa'uld symbiote inside a host. Then, the device is able to target the host and teleport them down into a specially prepared cave. Thor's Hammer is encountered by SG-1 right outside of the planet's stargate, so that all incoming travellers are scanned and dealt with before they can get away from the gate.

Once inside the cave, the Goa'uld/host are provided with a food supply and water. In order to leave the cave, the host must walk through a portal that has another device - which removes the Goa'uld symbiote and leaves the symbiote in t he cave. In this way, Thor's Hammer was able to protect the people of Cimmeria from Goa'uld invasion forces for many years.
-- Genetic manipulation/cloning --
The Asgard are able to genetically engineer clones and to manipulate cells to remove undesirable traits (such as disease). The trouble is that they are no longer able to reproduce sexually; they are only able to clone themselves. This cloning has limitations, especially in regard to the lack of diversity in the material being used. The Asgard are now experiencing a slow genetic breakdown as a race, and are trying to use their knowledge of genetics to stop it.
-- Cryogenic Stasis --

The Asgard have capsules (as shown above) that are capable of placing those within into cryogenic stasis. This freezes the body in place so that further degeneration does not take place: diseases stop in their course, aging ceases, and so forth. This is a great aid to those who are injured and need more medical care than can be provided at the time. It is also helpful in that the injured can be kept in stasis until a healer can see them.