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I always find people are not properly familiar with knots or how to tie them. Perhaps we should have a quick reference for people who would like to refresh themselves on how to tie or use common knots.
I was also thinking about making separate Wiki Articles for each.
There are a lot of different terms associated with knots. This could also serve as a home for them. I know a lot of people get confused with rope, and I feel it is something most people should be familiar with (if only to take garbage to the dump safely).

Please note this is NOT A RIGGING HOW TO! If you are not fully competent in rigging, stage or otherwise then DO NOT DO IT. However knots do have a home both inside and outside rigging.
Personally (Dionysus) I have been tying knots since I was old enough to tell the Bight from the End, or Live End. My grandpa was a sailor and engineer (I grew up with him almost like a Dad) and taught me a lot.

This thread will link to various WIKI articles on various parts.

Terminology:
Bight - Bend in rope or part away from an end.
Cinch
Cleat - Something used to hold a rope.
Dead End - One End of the Rope, usually the end carrying the load (not included in a knot)
Live-End - One End of the Rope, also called the Running End or Working End.
Overhand Loop - Both a Knot in its own right (Overhand Knot used as a Loop) or as part of the instruction in tying a knot. A loop is when the rope is laid over itself, a overhand loop being one where the cross is made in an overhand fashion.
Underhand Loop - Again part of an instruction of knot tying, or component in a knot. Same as an Overhand loop, however crossing the other way
Elbow - Creating a loop and continuing through a full rotation (half rotation for a loop).

Image http://upload.wikimedia.org/wikipedia/commons/thumb/a/a1/BightLoopElbow.jpg/220px-BightLoopElbow.jpg

Note on Strength of Rope and Knots:
Do not use this for rigging, but this is a good general idea to how much a knot degrades the strength of a rope.

100% Strength: No Knots or Splices
85% Strength: 15% reduction in general from proper splices
75% Strength: 25% reduction in general from hitches (Clove hitch)
50% Strength: 50% reduction in general from any one knot
50% Strength: Same goes for tying any two ropes together, or looped through eachother.
25% Strength: 50% reduction from one knot, 50% from another. TWO KNOTS! OH NO!
0% Strength: A POORLY DONE KNOT, by someone who is not a rigger ;)

Bowline Knots:
Bowlines are strong loops that are not "nooses" (ie they do not slip or "close"). By their very nature they tighten around the knot itself as loaded, holding tighter. A bowline that has supported a heavy load will be difficult to untie, but will never tighten around it's load.

Bowline
French Bowline
Running Bowline (closes or Chokes) - Useful if you are a cowboy (lasso).

General Knots:
Trucker's Hitch - Used to shorten a rope with mechanical advantage. Commonly used when a ratchet strap is not handy when loading a truck.
Belaying - Properly wrapping a rope around a cleat to hold it
Strap Knot - Used to knot two straps (leather) together
Toggle Hitch - Almost not a knot, uses a "toggle" to hold a line onto a ring.
Butterfly Knot - Also one of my favorites. A Loop (think bowline) tied easily on a bight that can take equal load in any direction! A REALLY COOL KNOT.

Nooses (Knots that close):
Slip Knot - Evil but sometimes useful. This knot can be easily tied or un-tied, or un-tie itself.
Noose - Essentially a Granny knot tied back on the same rope. Creates a slipping loop.
Hangman's Noose - This knot was used as a form of execution, it was tied to have a lot of resistance in closing (choking, no pun intended. Quite serious.) so that it would break the victim's neck, but if not succeeding would eventually cause death by strangulation. I have seen this knot used for various things, including hanging battens (I don't much care for it).

Bends: Knots for Joining two ropes together
Reef Knot (Square Knot)
Carrick Bend
Fisherman's Knot
Surgeon's Knot
Sheet Bend
Double Sheet Bend
Slippery Sheet Bend
Prusick Knot (often made a "sunday")
Stopper Hitch (Rolling Hitch, Bag Tie)

Hitches:
Single Blackwall
Double Blackwall
Cat's Paw
Mooring Hitch
Lash Knot
Clove Hitch
Two Half Hitches
Timber Hitch
Taut-Line Hitch
Fisherman's Hitch
Pipe Hitch - Used for holding loads vertical (like rising a pipe vertical)

End Knots:
Figure-Eight Knot
Stevedore's Knot
Wall Knot
Sheepshank
Single Matthew Walker
Monkey's Fist - (My Favourite)

Lashing
Diagonal Lashing
Square Lashing
Shear Lashing

Knots specific to the live entertainment industry
Used to attach a drape to a batten: shoelace knot, Opera knot.

Special Knots:
Underwriter's Knot - Ties a twisted pair of wires together.