In Quake, a Spawn or Tarbaby is an elastic blue blob that repeatedly flings itself at the player, doing damage with every slap. When a Spawn is killed, it lets off an explosion that deals high damage to anyone close by. Very dangerous on its own, but a nightmare in larger numbers. They are exclusive to the Elder World levels.
The Spawn has two attacks, a tackle slap-type attack where it flings itself at high speeds towards the player. The Spawn is dangerous in wide open rooms, but even more so in tight spaces. In the water is where the Spawn truly shines as the player's movements are severely limited, yet the Spawn seems unaffected when underwater, thus can continue its assault. Limited movement means that is it harder to get away from the Spawn, in order to kill it at distance. Any attempts at confrontation in tight areas should be avoided.
The Spawn is one of the most aggravating Enemies in the game. This is mainly because of its speed and the amount of damage it can inflict through the frequency of its attacks. In addition, the explosion it lets off upon being killed can take most of your HP in one shot or kill you. Therefore, you'll have to time the Spawn's movement so that it dies away from you. Shoot a rocket from a safe distance so that it explodes when the Spawn is jumping back after hitting you. A rocket's splash damage usually has enough power to kill it in one shot.
A group of Spawns are much easier to take out. As soon as you see them, take out your Grenade Launcher or Rocket Launcher and begin firing. In addition to the explosion, the splash damage from the exploding Spawn will hit other Spawns as well, causing them to blow up. If you do it correctly, you can cause a whole room of Spawns to die before they start attacking. With very big groups, like the ones in The Pain Maze, you may need to fire more than one grenade or rocket.
A Spawn with other monsters should be killed relatively quickly. One useful strategy is to try exploiting its explosion. Make it so that it dies when other enemies are nearby, as the splash damage can kill most creatures within its vicinity.
Spawn is one of the only three monsters (along with Vore and Shambler) that are capable of gibbing Zombies, usually with its death explosion.
According to John Romero, the Spawn was rare because it was conceived later on in Quake’s development and it was so tough that the designers could not use it frequently. 
There are some unused animations in the model files of the Spawn flying.
There is a possibility for a Spawn to become invulnerable if it manages to destroy a Radioactive Container and the Monster is not destroyed in the process. The Enemy counter will be updated as the entity is no longer seen as a Monster. The Spawn will instead be seen as a solid brush, like a wall, that will prevent its destruction while permitting it to continue to bounce around the world and damage its opponent. If the player tries to hit the Spawn with an Axe, the sound will be similar to that made when an Axe hits a wall. This can also happen with the Fiend but its even more rare and can only happen on custom maps such as killemall.bsp, the difference is that the fiend will only move by jumping and can't damage the player. 
The Spawn is a monster influenced by the Formless Spawn from Sandy Petersen's Guide to Monsters. Formless blobs of slime, they dragged their body forward with tentacle-like appendages sprouting in front of it. They're associated with the worship of Tsathoggua.
The Spawn spotting his enemy
The Spawn bouncing off a surface
The Spawn colliding with their opponent
The Spawn being killed
The Formless Spawn, the influence for the Spawn, from Sandy Petersen's Guide to Monsters