While a professional-grade camera (Canon 5D Mk II and up, Nikon D700 and up) is certainly a huge help for those who can take advantage of the features pro bodies offer, the most important tool is the photographer's knowledge. I currently shoot with a Canon PowerShot A590 IS (though I do not do professional work with it). I'm taking a 2-year break from paid photography work (and pro-bono work that would otherwise be paid). When this hiatus ends, I'll be upgrading to whatever camera sits in the slot the 5D Mk II currently occupies.
While I was shooting paid portraits, etc., I used the Canon Rebel XSi. Some pros sneered at my entry-level camera. My work sneered back at them:
http://www.flickr.com/photos/naturesmugshots/4521632221/in/set-72157622923292355/
http://www.flickr.com/photos/naturesmugshots/4823108736/in/set-72157622923292355/
http://www.flickr.com/photos/naturesmugshots/4421221148/in/set-72157622923292355/
The lens is still more important than the camera. Putting sharp, fast primes in front of the Rebel XSi will give better results than buying a 1D Mk IV and cheaping out on the lenses. Frankly, it's possible to take professional-quality photos with virtually any camera, if you know what you're doing. Camera upgrades mostly offer better features and more control over the image, more resolution, etc. Actual image quality bumps are fairly small between cameras after you get to the CMOS sensor.
Again—knowing your stuff is much more important than your gear. I took this picture with a Canon PowerShot A590 IS—a point & shoot camera that is so "outdated" that it hasn't been made for about 2 years.
http://www.flickr.com/photos/naturesmugshots/5463110472/
As far as flexibility... mostly it comes down to your lens choices. The sad truth is you need to have a pretty wide range if you want the sharp images that most people are after. Buying an "all-in-one" lens isn't a good choice if you want to do paid work. The four lenses I use the most are the 50mm f/1.4, the 85mm f/1.8, the 100mm f/2.8 Macro (non L version) and the 135mm f/2L. I like my primes.
Good luck!