Occam's Razor essentially says that all things being equal, the simplest solution is the best. The principle has implications in virtually every field of science, not to mention philosophy, aesthetics, marketing, business, you name it.
If for some reason you don't buy the word of a 14th-century Franciscan friar, it might interest you to know that Albert Einstein also believed the universe loves simplicity. I don't know about you, but I'm in no position to argue with that guy.
You'd think that keeping things simple would be the easiest path, but that's not necessarily the case. Sometimes it's downright impossible. Look at the personal computer, for example. The need for backwards compatibility with legacy programs and interfaces has forever rendered the PC more complex than any of us would like.
Some people have a knack for making things more complicated than they need to be. I've found that to be the case particularly with people who make incorrect assumptions and then get intertwined in an endless but futile effort to prove themselves right.
Johannes Kepler had the laws of planetary motion in hand for years, but he refused to recognize them as they conflicted with his notion that the planetary orbits were inscribed in perfect solids - polyhedra with symmetrical faces, edges and vertices. At one point he even fudged data to support his theory. He would almost certainly have discovered the law of gravity ahead of Newton had he not been so wrapped up in his misguided pursuit.
For some folks, simplicity appears effortless. Lou Gerstner executed one of the most challenging turnarounds in business history by reversing the planned disaggregation of IBM and refocusing the company on IT services. His new vision for big blue was brilliant, but it was also simple and elegant, requiring far less restructuring than the previous plan.
Too bad Yahoo's board replaced CEO Terry Semel with Jerry Yang instead of Gerstner.
Google's founders had great difficulty getting the company off the ground because nobody - not even them - thought search could be a big enough business on its own. Ironically, Yahoo-founder David Filo encouraged them to start a search-engine company. Who thought something so simple could generate so much dough?
Even job searches are a good example of how simplicity works best. The best resumes are short and succinct. A great way to self destruct in an interview is by going on and on and digging yourself a hole that the interviewer can exploit. If a particular job or field isn't working out, most people will stick with it way too long instead of doing the obvious thing and trying something different.
Then there's my personal favorite. There's nothing more annoying than a 50-slide presentation with a dozen bullets and sub-bullets and a book of text on each slide. Drives me crazy.
In summary, keep it simple. And if you find things are getting too complicated, then change your assumptions and try again. All the best things in life are simple. Really.