The challenge for any company built on innovation is keeping the innovation flame burning. History tells us that even the most innovative companies don't keep the flame burning for long, and there are signs that that time may be coming to an end for Google (Nasdaq: GOOG).

Google is still a great inventor; that I am not questioning. It can come up with ideas with the best of them. But when I wrote the intro to our "Innovation in America" series, I distinguished the two by saying that "invention is the process of turning money into ideas; innovation is turning ideas into money."

When it comes to turning ideas into money, Google peaked when it came out with AdWords and AdSense (technology it actually acquired) years ago. These revenue streams, driven by the company's algorithm to match content with relevant advertisements, still dominate the company's revenue and are basically the foundation of Google's fortress-like moat.

Efforts to expand the business have been fun and entertaining for those of us using Google products. Google Earth, Gmail, Google+, YouTube, and other applications are fun and productive, and they're great inventions, but they don't drive revenue for Google the way that search does. In this respect, Google is really a one-trick pony, and everything else it does is just an attempt to drive traffic to capture advertising revenue.

Even the emerging smartphone business, where the company has a dominant position, doesn't make the company significant money. Unlike Apple (Nasdaq: AAPL), Google has yet to turn this invention into an innovation, instead relying on smartphone users viewing ads on the Web, YouTube, or another Google ad placement mechanism.

Acquisitions gone wrong
The first major sign I look for that a company is loosing its innovation edge is a company focusing more on acquisitions than growing new products in-house. When Google agreed to buy Motorola Mobility last year, it was just the latest in a long line of product expansion acquisitions that kill innovation and suck the life out of a company. If this week's news that 4,000 jobs would be cut from the newly acquired company is any indication, the deal may already be running into challenges.

Recently the company added Frommer's and Wildfire Interactive to its ranks, costing nearly $500 million in total. Since the start of 2010, the company has made an astounding 60 acquisitions, nearly one every two weeks. This isn't what a company building innovative products does.

For an example of what happens to an innovative company over time, Hewlett-Packard's (NYSE: HPQ) challenges can be traced back to when it purchased Compaq, a company that changed the company's focus from innovation to operational excellence in a commoditized business. The company that began in 1937 survived by constantly reinventing itself through innovation, something it has failed to do in the past decade.

Innovation fades fast on the Internet
If you think Google's position atop the Internet's food chain will last forever, just look at history. Yahoo! was once the dominant search engine, MySpace was the innovative social network before Facebook (Nasdaq: FB), and Geocites was the most popular website in 1997.

Things change fast, and Google doesn't seem to be coming up with new businesses that will pad the company's results the way a competitor like Apple can. Instead it's relied on acquisitions, not a normal strategy for a company that's supposed to be an innovator.

Foolish bottom line
Google will continue to grow along with the Internet -- that I don't question. What I am wondering is whether the company will ever be able to branch out beyond search-based products the way innovative companies before it have been able to do.

Google throws a lot at the wall, and some things stick to become useful inventions, but the company's list of moneymaking innovations are few and far between. Google may be the greatest inventor in Silicon Valley, but when it comes to innovation it isn't in the same vicinity as Apple.

So, how has Apple been able to innovate and stay ahead of the competition? Our Apple analyst discusses the company's incredible rise and how the company can stay on top in our report on Apple. Find out more here.