Grip strength can have alot of affect on the amount of weight you can lift in the gym. Grip training will much increase strength and size of your forearms. So, onto why you should improve your grip strength.
Builds Up Martial Arts Skills:
The power in which you can punch will greatly increase when using grip training. So if your a boxer and want an extra advantage over the opponent, grip training is a sure fire way to achieve this adavantage. Also, when it comes to grappling in martial arts, when you are gripping an attacker you might acquire an injury if your forearms/ gripping strength is/ are not very strong. This is also applies to when street fighting. Not that I'm saying you should go out and
find someone to fight after training your grip strength. That is not the reason for this training but will help if you ever have to fight someone. Usually in street fights its not about who can punch the hardest, it is usually who has the best choke hold and grip strength training helps with this.
Enhances Your Size For Bodybuilding Uses:
Enhancing your forearm muscles is key if your trying to become a professional bodybuilder. You dont wan't any parts of your body looking un-symmetrical. So if your a bodybuilder with not quite up to scratch forearms, then you need to train your grip strength!
Different Grip Strength Types:
So how many types of grip strength are there exactly? The answer is just two! These are Crushing Strength and Pinching Strength.
Crushing Strength =
This type of strength is made evident when someone crushes a can. This can also be made evident simply when you shake someone's hand! The forearm muscles being targeted when doing a gripping action is mostly the flexors but the extensors are also being targeted, just less than the flexors.
Pinching Strength =
When it comes to the real world the uses for pinching strength is very limited but it should still be training to give your forearms more size and it will increase finger and thumb strength. Pinching exercises are more difficult to train for than the crushing exercises. This is because the exercises are more awkward to do and just plain harder.

Holding Grip:
The thumb, fingers and palm is included in this kind of grip. The holding grip has alot of real life uses such as driving a car or holding an attacker in a fight.
Examples of Gripping Movements =
Grip Hangs, Towel Grip Dumbbell Curls, Towel-Grip & Plate-Grip Farmers Walk, Static Barbell Hold, One-Arm Dumbbell Rows With Towel, Rubber Ball Squeeze, Newspaper Balls, Newspaper Tearing, Fingertip Push-Ups, Wrist Twists.
As you can see there is a huge variety of different exercises to train your gripping strength, it is up to you now to try each exercise and see which work best for you and to make your own specialized workout program. It would do you no good following a workout program I have made since different reps, sets, rest times, etc. work for each unique person.

Author's Bio: 

Author of fitness and bodybuilding articles with 8 years of experience in health and fitness. Also has experience in household items such as wood storage shelves, Nursery Shelf and Hanging Glass Shelves items.