Hint: it's not a new camera.

The camera manufacturers, as well as many well-known photography gurus on the internet, would have you believe that the best way to improve your photographs is by upgrading your camera. It's certainly to the benefit of their pocketbooks to promote buying and selling gear, but unless you have money to burn and you're shooting with an outdated digital camera (let's say more than 7-8 years old), they're giving what is poor advice for most people.

In reality, the best way to improve your photographs is to carefully study the work of the long established masters of the craft. Understanding what makes a great photograph, and incorporating those concepts into your own work, is infinitely more valuable than increasing the number of megapixels on your camera sensor.

Here are a few of the artists whose work I've been studying in recent years:

Edward Weston
Minor White
Ansel Adams
Eliot Porter
Imogen Cunningham
Michael Kenna

Who you choose to study should be based upon your own interests and where you are on your path of discovery. The most important thing is not the particular photographers (there are many greats), but that your energy is directed toward understanding images, not acquiring gear.