The Reef Knot Family
The reef knot or square knot is notably dangerous if misused.  The square knot or reef knot should only be used as a binding knot where it lies tightly against the surface of that which it binds and cannot move. 

Unfortunately, it is wrongly used as a
bend where it can be deadly.  Used as a bend, joining two ropes, it can unexpectedly spill.  What's worse is that it often times holds firm so as to give people a false sense of security, thus setting the stage for tragedy when it shows its true unstable nature.  Even minute differences in rope size, texture, or stiffness in what most would consider "normal" rope, will greatly amplify the insecurity of a reef knot used as a bend.   It's also very vulnerable to spill when being pulled around corners or over rough terrain, especially if a free end gets snagged.

If you know how to
tie your shoes, you probably use a "slipped" form of the square knot or the granny knot.  The reef knot is handy as a binding knot and can often be undone by firmly jerking in opposite directions the free end and standing part of one of the "U" shapes that interlock to make this knot.

For greater binding or clamping force, carefully make multiple tight coils around your object or objects before finishing with a reef knot.  The power of friction will assist you in maintaining the tension in each coil as force builds up.   

A surgeon's knot or ligature knot is just a square knot with a double tuck on the first half of the knot instead of a single tuck.

The thief knot is usually more of a trick knot than anything.  It has the same general form as a square knot, but the pull goes diagonally across the knot.  This knot is supposed to fool a thief into retying a square knot after plundering a sack, thus alerting the owner.  It's more awkward to tie than the reef knot, and generally doesn't perform its binding task as well. 

The granny knot is generally considered a mistaken attempt at a reef knot.  It's easier to tie because you tuck the same way for both "halves" of the knot, but is a lousy knot for just about any purpose as it lacks security and will jam easily.

The grief knot, also called the whatnot, is a combination of the general form of the granny knot with the diagonal pull of the thief knot.  This is decidedly a trick knot.  Go ahead and tie one.  When you apply tension, it often rolls apart as if the knot isn't even there.  Some magicians use this knot.

The grief knot or whatnot has a dual nature.  Without untying the knot, you can twist the two free ends just like turning a key to make a completely different knot that has good security.  Magicians, with sleight of hand, can thereby make a firm knot out of something that had no security whatsoever before.  The Ashley Book of Knots describes this in detail.

The question arises as to whether this secure form of the knot could be used as a bend.  I'd recommend against it.  It doesn't strike me as safe to have a knot that, with the roll of an unlucky footstep, or with the innocent handling of a novice, could turn into a knot that looks snugly tied but has no security.  It's not worth the risk, especially when there are so many safe and effective bends you could use.