A classic test of grip strength is how hard can you squeeze down with your hands. For this reason grippers were built to train and build this strength. These are not your average gripper! In the modern days, Ironmind has pioneered this movement with their grippers, ranging in strength from 60 lbs. (the Guide) to 365 lbs (the #4) and everywhere in between. There are also a number of other companies making grippers like the Monsters of Mash.
The Captains of Crush Grippers
These get so difficult that only a handful of men have certified on the #4 gripper, including Joe Kinney, Nathan Holle, David Morton, Tommy Heslep and Magnus Samuelsson. The current list, as well as rosters for the #3.5, #3 and more can be found here.
The following video shows Juha Harju closing the gripper, but not in certification style.
One of the basic motions of the hand, it is wise to have this somewhere in your training plan. Not just for being able to open that jar of pickles but as a necessity in many sports, especially the combative ones.
The important thing is to work to close the gripper all the way, so that the handles are touching.
At the highest levels a crushing grip can not only close a tough gripper but pulverize an apple or potato with one squeeze of the fist as shown by Tommy Heslep here.
There are also other forms of the gripper challange, like the silver bullet hold. Here a #3 gripper is held closed on the silver bullet, with a 5.5 lb. weight hanging from it, as shown by strongman Mark Felix.
For more details on closing grippers, see the following: