The Collector cruiser first appeared just a couple of months after the Battle of the Citadel, ambushing the SSV Normandy SR-1 in the Amada system, over the planet Alchera. The Normandy was destroyed and 22 crew members were killed, including Commander Shepard (s/he got better).
Over the next two years, the ship (and possibly others like it) raided human colonies in the Terminus Systems, abducting the colonists almost without a trace. The Collectors were not linked to the disappearances until a quarian pilgrim was found alive following their attack on the Freedom's Progress colony.
The ship was later "caught in the act" of raiding the Horizon colony, but Commander Shepard intervened before the raid was complete, restoring the colony's anti-ship defense batteries and driving the Collector ship away before all of the colonists were taken.
The Collectors later attempted to kill Shepard by using the ship as bait, sending a false message that turian warships had disabled it, but been forced to retreat themselves. Shepard intercepted the "derelict" ship with the Normandy SR-2, and his team boarded it. When the trap was sprung, they were nearly captured, but they managed to fight their way back to the Normandy and escape before it was fully re-powered.
When the Normandy later attempted to install a Reaper IFF device, it introduced a virus into the Normandy's systems that shut down the engines and signaled their location to the Collectors. The Collectors soon found and boarded the ship, and only quick action by Joker and EDI kept them from taking the ship, but the rest of the crew was abducted (Shepard and the ground team were off the ship during the attack).
The Normandy encountered the Collector cruiser again after passing through the Omega-4 mass relay. In this final confrontation, the Normandy was able to destroy the Collector vessel.
A small number of similar vessels were encountered during the Reaper invasion of 2186.
The Collector cruiser has a heat signature similar to the cruisers of other Mass Effect races, as the scan operator of the SSV Normandy quickly classed it as a cruiser, despite its unfamiliar configuration. It's actual volume and mass are much greater, comparable to a dreadnought. Despite its large size, it is capable of landing on a planet's surface.
The Collector cruiser's hull appears to have been built from an asteroid, as large portions of it appear to be natural rock. The basic shape of the ship is a tube, with engines on one end and an enormous weapon port on the other. Much of the ship's interior is a hollow cavern lined with the pods that the Collectors use for transporting captured colonists. Floating platforms allow rapid transport within this space.
The ship is armed with a massive forward particle beam and several smaller side beams. The forward weapon was powerful enough to cripple the SSV Normandy SR-1 with just a couple of hits. It is not clear whether it would have been as effective against a larger warship with thicker armor, since the Normandy still retained limited maneuverability even after several hits. It's primary advantage is that kinetic barriers provide no protection against it. In addition, it is capable of firing off axis, unlike the spinal mass accelerator of a dreadnought.
For defense, the cruiser uses kinetic barriers, but these proved to be insufficient against advanced weapons like the Thanix cannon or disruptor torpedoes mounted on the Normandy SR-2. Overall, the ship seems to be designed more as a transport than a warship, despite its powerful weaponry.
The sensor systems of the Collector cruiser are advanced enough to overcome the experimental stealth technology developed by the Systems Alliance.