In the Teenage Mutant Ninja Turtles world, mousers were robotic rodent-catching machines with a small degree of artificial intelligence, so that they could be given general orders from a central command unit and left to carry them out unattended. They were invented by Baxter Stockman in the original comics, the 80's cartoon, and the new cartoon series, but do not appear in the live action movies.
Physically, mousers were small white robots with two legs and an oversized jaw that looked something like a bear trap with only three teeth. The overall impression was that of a very small Tyrannosaurus Rex except without any forearms at all. The original design intention was to create a robot small enough to follow rats into hard to reach places, and devour them. Each mouser had a "stomach" capacity of three or four average sized rats, and when full it would return to its controller to be emptied and sent back out for more rats. They were designed to be unleashed en masse to kill rats faster than they could breed.
In the comics, Stockman invented the mousers publicly to solve the city's rat problem, but secretly to rob banks and threaten buildings with collapse to hold them for ransom (the mousers were somewhat over-designed in that they could chew through concrete and steel). In a demonstration, Baxter showed that the small robot could go virtually anywhere a rat could go, and even chew through the walls of a the maze he set up to get at the rat. What nobody realized was that it could just as easily chew through the wall of a bank vault and swallow bags of money. When his assistant, April O'Neil (occupying a very different role than she did in the cartoon), discovered this, she attempted to tell the police but Baxter sent the mousers after her. The Teenage Mutant Ninja Turtles rescued her just in time and returned to stop Stockman with her help, but when they returned to the lair they discovered their sensei, Splinter (who is a giant mutant rat), had been attacked by the rat-seeking robots and was missing.
The new cartoon follows the comics pretty closely.
In the 80's cartoon, Stockman tried to use the mousers legitimately but was turned down by the pest control industry because the robots would have put them out of business. The Shredder was interested in his invention, however, seeing in them a perfect weapon with which to attack his old rival, Hamato Yoshi, the Turtles' sensei, now mutated into a giant rat. Note that the comics Splinter was a pet of Hamato Yoshi, while the cartoon Splinter was Hamato Yoshi himself. Using Krang's advanced technology at the Technodrome, Shredder was able to reproduce hundreds of the mousers from Stockman's prototype, each one exactly the same in every detail. Splinter was able to fend off the first few that attacked, but when the next dozen of them arrived only the timely intervention of the Turtles saved him. The Turtles quickly tracked the mousers back to their creator because Krang's machine reproduced the prototype too perfectly: including the engraved message "Baxter Stockman, inventor". In the end, the hoard of mousers are defeated with the help of Krang, who tells Michaelangelo where to find the control device because he wants Shredder's plans to fail. At this point in the series Shredder hadn't built Krang's android body yet, and he was getting impatient.
In the video games, the mousers tend to be low powered cannon fodder enemies, attacking in large groups and destroyed with only a few hits — really only intended to whittle the player down for the confrontation with the level boss. The mousers tend to attack by biting the player with their steel jaws, latching on and not letting go until they are shaken off by wiggling the joystick and mashing the buttons.