The grappler was a metal cable with an effector on the end that could be launched by a starship to grapple objects in space. The grapplers utilized a magnetic lock device to clamp to objects.
The grappler system of an NX-class starship
The NX-class starships of Starfleet were equipped with two grapplers. However, their use was eventually superseded by the development of the superior tractor beam. (Star Trek: Enterprise)
22nd century Starfleet shuttlepods were also equipped with a grappler on their aft section. (ENT: "Similitude")
Shortly after its launch in 2151, Enterprise used the grappler to capture a Suliban cell ship, which was evacuated by its lone Suliban occupant and brought aboard Enterprise. The ship was then used by Enterprise crew to infiltrate the Suliban helix. (ENT: "Broken Bow")
Enterprise grapples a D5-class as an improvised battle tactic
Vidiian ship deploying grapplers
In the same year, Enterprise encountered a hostile alien ship, that used a grappler-like technology. (ENT: "Fight or Flight")
Later that same year, Enterprise Captain Jonathan Archer attempted to use his ship's grappler to retrieve Shuttlepod 1, which had fallen into a chasm within Archer's Comet. Although only one of the two grappler claws latched onto the shuttlepod, it proved sufficient enough to reel the craft back to the ship. However, the eisillium in the comet's composition began to disrupt the grappler's magnetic lock, and Enterprise was forced to lower and release the pod before the connection broke. Fortunately, a Vulcan ship was near by to offer assistance, and following a reluctant request by Captain Archer, the Vulcans were able to retrieve the shuttlepod using their starship's tractor beam. (ENT: "Breaking the Ice")
Also in 2151, Enterprise again used the grappler to retrieve its own shuttlepod after it had been stolen by a female Klingon. Three Enterprise crewmembers had used the pod to board a Raptor-class scout vessel, the IKS Somraw, which was sinking into the atmosphere of a gas giant. The ship's engineer, Bu'kaH, hijacked the pod, stranding the three crewmen aboard her endangered ship. She then attempted to contact her people to falsely blame Enterprise for the attack on her ship which landed it inside the gas giant, but the pod was captured via the Enterprise's grapplers and Bu'kaH was brought aboard. (ENT: "Sleeping Dogs")
In 2154, Enterprise successfully disabled a pursuing Klingon D5-class battle cruiser by using the grappler to shear its port nacelle until the vessel could no longer generate a stable warp field. (ENT: "The Augments")
The Orions also utilized grapplers on their ships, such as aboard an Orion barge. (ENT: "Bound")
Majalan combat cruisers were equipped with grapplers as of 2259. (SNW: "Lift Us Where Suffering Cannot Reach")
Both La'an Noonien-Singh and Brad Boimler were enthused about grapplers. (SNW: "Those Old Scientists") Due to this, the "lower deckers" of Cerritos added a grappler onto Sequoia (LD: "A Few Badgeys More").
The swarm species used similar devices on their ships to clamp onto and attach themselves to the hulls of trespassing vessels and drain energy from them through their hulls. (VOY: "The Swarm")
The Vidiians made use of a similar technology on board their starships in 2371 and 2372. (VOY: "Deadlock", "Fury")
Pakled ship grapplers
By 2380, Pakled Clumpships were equipped with massive grapplers, used to restrain and tear apart other starships for their technology and materials. (LD: "No Small Parts")