Do not assume that all useful knots have been discovered.  Some really great but previously undocumented knots get discovered regularly.  Although helpful, you don't need extensive knowledge of how knots work.  Here are some techniques that may allow you to find some of your own:

Inverse Knots:  If you pull on the free ends of a bend or hitch, leaving the standing parts slack, you're revealing the knot's inverse.  Some knots are their own inverse.  You can apply the concept to loops to form the inverse or a partial inverse of the loop knot by changing the load path.  Of course, you can also make partial inverses of bends by only switching one standing part and free end.  This method works best with short rope.

Type Migration
:  Found a nice bend?  Try tying it as a loop by joining a free end with a standing part to form the legs of a loop.  In fact, many hitches, bends, and loops can be transformed into the other knot types.  By type migration, the Bowline is related to the Sheet Bend, Pile Hitch and others.

Loose Manipulation
:  This method goes hand-in-hand with the previous method, but may be used on its own to uncover different functional knots.  As the name implies, you merely keep the knot form very loose as you attempt to move parts around into other configurations.

Retucking & Augmentation:  Use the existing structure of known knots to provide the basis for experimenting with different knot forms.  By untucking the last pass of a Constrictor Knot, and retucking the end from the opposite side, the Sailor's Hitch appears.  With the advent of synthetic materials, many knots were simply carried further to increase friction through augmentation, but you can also continue tucking the end of the rope of known knots to make very different (and occasionally simpler) knots.

Starting Position Permutation:  On the Rosendahl Bend page, you can see how non-interlinked "b" and "q" shapes are the foundation of the bend.  Try various permutations of "b", "q", "d", "p", "s", "u", and other shapes. 

Criteria For Success
Ease of Tying:  For better or worse, this is the most important factor that determines whether a knot will see wide use.  Many knots that perform poorly in quite a few categories are nevertheless used routinely because they can be tied so easily.  If you can think of an easier way to tie a documented knot with remarkable attributes, this can be a greater accomplishment than discovering a unique knot.  Transforms, like the multiple coil method, can often make knots simpler to tie, such as the Farmer's Loop, Butterfly Loop, Boa Knot and the Perfection Loop used by some anglers. 

Memorability:  This is closely related to the previous category, but slightly less important.  A knot can be easy to remember but still be awkward to tie.  While knot symmetry isn't required, it can help make a knot more memorable.

Jam Resistance:  An important attribute, discussed at the end of the Notable Knot Index FAQ's.

Security & Stability:  Significant attributes, discussed at the end of the Notable Knot Index FAQ's.

Strength:  A lesser consideration in rope, discussed at the end of the Notable Knot Index FAQ's.
If you come up with something, contact me and it might end up on this site.
Discovering New Knots