
Heat to the Rescue
Heat, oil
and tapping will unstick most nuts and bolts in metal. Apply only
enough heat to cause expansion in the entire bolt—about a minute or so
for the average-size bolt. When the bolt is cool enough to touch,
squirt penetrating oil (it comes
in a spray can or squirt bottle) on and around it—and the nut if it’s
accessible. Be careful, that stuff is flammable. Tap the end of the
bolt a half-dozen times with a hammer to help loosen the threads and
allow the oil to penetrate. Wait another minute or so for the oil to
work, and then use your wrench.
Get a Grip
When a bolt head has become so rounded that a wrench won’t get a bite,
use a locking pliers. Get a tight grip: You may have only two or three
chances before the head gets so rounded that even this won’t work. Use
penetrating oil, heat and tapping if it slips after your first try.
Adjustable Wrench Technique
An adjustable wrench isn’t the ideal tool for loosening stuck fasteners
because it can round over the head, making matters worse. But if an
adjustable wrench is your only option, here’s your best shot at
preserving the shoulders on the nut or bolt head: Slide on the wrench
all the way, so there’s full contact at the back of the jaws. Then
tighten the wrench thumbscrew so there's no play at all in the jaws.
Always turn the wrench handle toward the lower jaw, never away from it.
Mangled Slot, Solution 1:

If the slot of a roundhead screw or bolt is chewed up beyond hope of
gripping it with a screwdriver, file two flat edges on it. Then turn
the head with an adjustable wrench.
Mangled Slot, Solution 2:

Use a hacksaw to cut a new slot at a right angle to the old one. For
big screws, put two blades in your hacksaw, right next to each other,
and cut a wider slot so you can use a big screwdriver. This is also a
great way to get a grip on the head of a stuck
carriage bolt, which has no slot or flats.
Off With Its Head
When there’s no other solution—when heat, penetrating oil and wrenches
have all failed—cut off bolt heads or nuts with a hacksaw,
reciprocating saw or a cold chisel. Some smaller fasteners, especially
rivets and flat head bolts, may
be easier to drill out than to cut.
Sticking Screw
A wrench on a screwdriver blade will help beat that big screw that
won’t budge. First select the largest screwdriver that’ll fit, and tap
the butt of the screwdriver handle with a hammer to loosen the thread
bond. Lean your weight onto the
screwdriver to keep it in the slot as you turn it with the wrench.
Careful—too much torque will bend the screwdriver tip.

And since we’re talking about force, a word here about sockets: You’ll find that six-point sockets get a better grip on hex nuts and bolts than garden-variety 12-point sockets, which are designed to fit both hex and square fasteners.
CAUTION:
the cheater bar technique can exceed the design strength of the tool,
cause it to break and void the tool warranty. Wear eye protection.
Split a Nut
A nut
splitter will crack any no-go nut without damaging the threads of the
bolt or stem that it’s screwed onto. Just slip the ring over the nut
and turn the tooth into the nut until it breaks. Find it at Sears (part
No. 94772) and other tool stores. Cost: about $15.
A Screw Extractor

A screw extractor could save your day. It will grab just about any
threaded fastener and remove it—even if the head has snapped off. It
usually comes with a hardened drill bit to drill a hole in the center
of your stubborn screw or bolt. Then
you turn the extractor counterclockwise into the hole. Because of its
tapered shape and lefthand thread, the extractor will jam in the hole
and then begin to turn out the screw. Cost: about $6 at hardware stores
and home centers.
Impact Driver
An impact
driver works with a bladed or Phillips-head screwdriver bit, or a
socket head. Striking the tool does three things at once: The blow
loosens the thread bond; the downward force keeps the tool in the slot;
and the head of the tool turns 20 degrees in the loosening direction.
Make sure the screw slot is clean and free of debris. Find it at Sears
(part No. 47641) for about $20.