I fully agree with Delta-Sys that every tool box should have at least one pair of vise-grips. However, there is a time and a place for everything and sometimes they aren't the right tool.

When to avoid using vise-grips:
  • Turning nuts or bolts
    An adjustable crescent wrench will manage, a box wrench or socket wrench of the proper size is best. If you don't have quite the right size (metric bolt, customary wrenches), locking pliers might be better.
  • Turning screws
    That's what a screwdriver is for. If you don't have the right driver, keep in mind that you severely shorten the lifespan of the screw. If it's never returning to the material from whence it came, vise-grips are fine.
  • Clamping soft materials (wood, plastic)
    They give little feedback and you can easily destroy the items you are clamping. An actual vise appropriate for the material in question should be used. If you have extra material and can test the pressure, you may be able to get away with minimal or no damage.
  • Cutting or tearing
    Bad, bad, bad. The use of pliers as a cutting implement is not only horribly inexact but will most likely leave jagged edges on the material in question. Unless you are trapped in a small metal box with nothing else, try to find an appropriate cutting tool.
Beware of over-tightening!

Vise-grips can exert up to a full ton of force. On most models this is concentrated onto less than 1/4 in² of area for more than 8000 lbs/in²! Your average nut can be horribly deformed by this much pressure. Be especially wary of this in DIY jobs since most prepackaged fasteners from ACE or Home Depot are made of rather soft alloys.

Beware of the limits of your other tools.

A pair of vise-grips can be used to give added torque to a screwdriver but make sure you are using a real screwdriver (Craftsman, Snap-On, Matco) and not one purchased at a dollar store. Craftsman is especially good since Sears will replace any Craftsman tool if broken, free of charge and no questions asked.

When vise-grips will save you time, energy and aggravation:
  • Extracting a stripped or damaged screw or bolt. Locking pliers can give you a very good grip and besides, you're not reusing the screw anyway.
  • Welding. Vise-grips offer the speed and strength for continuous work. Using a standard screw type clamp can get very tedious.
  • Space is an issue. Vise-grips use very little space compared to regular clamps and can get into places your average wrench may have trouble with.
  • Very temporary, test anchorings are needed. For example holding a car part in place to see if it vibrates and/or behaves properly.
  • Storage space is a problem. Vise-grips can be very handy in a dorm room or small office where keeping a good tool box would be inconvenient.
Specific Vise-grip models and their primary uses:
  • Curved Jaw, 7" or 10"
    General use pliers, usable as pipe wrench, all-purpose clamp.
  • Curved Jaw with Wire Cutters, 4", 5", 7", or 10"
    Same as above with wire cutters. Wire cutters may be useful for very heavy gauge wire
  • Straight Jaw, 7" or 10"
    Good for use on square or hex nuts and bolts, clamping and metal work.
  • Long Nose with Wire Cutters, 4", 6", or 9"
    Good in small areas, ideal for precision applications and hobbies.
  • Bent Nose with Wire Cutter, 6"
    Tightening or removing bolts in cramped spaces, hobby applications.
  • Large Jaw, 6" or 12"
    Plumbing, car repair, welding.
  • Locking Wrench, 4", 7", or 10"
    Adjustment of various sized hex bolts, extraction of hex fasteners.
  • Locking C-Clamp, 6", 9", 11", 18", or 24"
    Wide jaws provide access to hard to reach areas. Useful in metalworking, auto body repair.
  • Locking C-Clamp with Swivel Pads, 4", 6", 9", 11", 18", or 24"
    Same as above with swivel pads to provide better contact with materials.
  • Locking Hold-Down Clamp, 11"
    Locks onto a table or workbench to hold irregular materials. Has a swivel pad to prevent damage.
  • Locking Bar Clamp, 10"
    One jaw adjusts freely on a bar to provide much wider grips.
  • Locking Welding Clamp, 9"
    Holds two items for easy welding.
  • Locking Sheet Metal Tool, 8"
    Recommended for metal and upholstery work.
  • Locking Panel Clamp, 9"
    Holds thin materials. Ideal for metal work and auto body repair.
  • Locking Chain Clamp, 9" (18" Chain)
    Locks around almost any shape. Good for plumbing, auto repair.
  • Locking Pinch-Off Tool, 7"
    Designed to pinch off tubing and hoses.
In the event that the proper tool happens to not be vise-grips and you do not have the proper tool, than by all means use vise-grips. Unless, of course, the proper tool is only 10 minutes and $5 away, in which case you might consider taking that extra time to acquire said tool. It may be cheaper in the long run. Vise-grip locking pliers are very good tools, but please, use them responsibly.