Necessary: Any sort of camera, including that on a phone. But then, I've seen some really bad real estate photos.
It seems to me that a good proportion of agents & sellers simply do not care how their listing photos look. It seems crazy, given that a house is very visual and very expensive. When I was house hunting, I saw lots of low resolution, mis-exposures, poor color, bland lighting, flat angles, yuck. When I was selling, my agent snapped photos with a $100 camera from Best Buy.
But consider that many (most?) listings have photos taken by someone with little skill or interest in making nice-looking pictures. And the agents aren't in a rush to spend money to improve upon that. So extra equipment would go wasted in those hands.
Now... I'll assume that you're not working with agents like this, since you're talking about making it a part of your career. Presumably you're photographing higher-end housing, and so have higher-end skills and thus can make use of higher-end equipment.
- A (ultra) wide-angle lens, ideally zoom. Nothing makes the angles of architecture stand out like perspective distortion. It'll make the rooms look larger too, which is a big boost for real estate. A lot of times you'll be in close quarters too (think: closet) and this is what ultra-wide angles do. I have a 10-24mm on my Nikon D90 (EFL 15-36mm) and it seems exactly right for walking around the house.
- An off-camera lighting kit: Light stand, flash, wireless trigger of some sort, and probably an umbrella. Natural light might not always be in your favour, and on-camera flash looks flat and harsh. I'd go with a radio trigger so that you can hide the flash around corners without hassle.
- A DSLR, so that you can use the wide-angle lens and off-camera-lighting to their fullest. However, there's not a lot of need to get fancy here; the camera will be tertiary to the lens and the lighting in order of importance. Remember that your photos are going to be shrunk down to fraction-of-screen-size (unless you're doing big prints or magazines; that's a different story); you don't have to be tack sharp necessarily. A non-DSLR (esp. micro-4/3) would be OK too, as long as it can support the lens and lighting.
Beyond that, I don't think there's much else. A tripod might help but it's probably more hassle than it'd be worth.