First of all, I'd like to explain that I'm a Canon user for no other reason than it being the brand I started with (my first camera was the Rebel T1i). There are many subtle differences between the top brands but I won't get into them here as there are countless articles out there that have beaten the subject to death. For what it's worth, I've been very happy with the Canon brand but am sure that other brands, such as Nikon, would have no problem taking the photos that I want to as well.
Canon 6D: (http://goo.gl/y7QvS7)
For the most part, I shoot indoors at night so I need a camera with great low light performance. I recently bought the 6D as an upgrade to replace my 5D Mark II for photography. Being a newer camera, the 6D outperforms the 5D II in every aspect that matters to me - low-light performance, burst frame-rate, and dynamic range. The 6D's full frame sensor performs very well at high ISO and I can comfortably shoot up to 3200 without too much noise and color distortion. The faster burst-rate, although a small difference (4.5 versus 3.9 fps) is nice to have for fast-moving subjects. I love to take landscape photography in my free time so improved dynamic range is also very welcomed. The 6D's sensor is rated at 12.1 EVs compared to the 5D's 11.9 EVs. This might not sound like much but I've found that you can squeeze a lot of shadow and highlight detail out of the 6D RAW files. The build quality of the 6D isn't as high as the 5D Mark II, but I actually like that it's a bit smaller and lighter as I need to move around a lot during a gig. With that said though, I probably wouldn't trust taking this camera out with me in the pouring rain as I've definitely heard horror stories (http://goo.gl/kOb5Th). Lastly, the 6D comes with Wi-Fi capabilities and although I haven't used it much yet, I'm thinking it will come in very handy for remote shooting as it can be tethered to a smartphone.
Canon 24-70mm 2.8L: (http://goo.gl/L027fE)
This is my bread and butter lens. I use it pretty much 99% of the time for its versatile zoom range, very quick auto-focusing, and image sharpness. All these features are vital to me because I primarily shoot events and can't afford to miss fleeting moments. The zoom range allows me to take photos of large groups and then switch to shooting solo portraits without a lens change. Since its aperture can open up to f2.8, it also performs well in dark environments and produces very nice bokeh. As it is an 'L' lens, the build quality is excellent and even rivals the sharpness achieved from some prime lenses.
Canon 580EXII: (http://goo.gl/0jeR5T)
When I started, I bought a Sigma-610 flash head figuring that a budget flash was good enough. Although the performance of the flash head was okay, the build quality is what led me to regret the decision. The hotshoe mount on the Sigma flash was made of plastic, and the mount has broke on me not once, but TWICE, resulting in me having to buy two now broken flash heads. The 580EXII is by far the best flash head I've used. It has excellent build quality. The hotshoe mount is metal instead of plastic, and has a rubber gasket sealing the contact point. The controls are also very easy to adjust, giving me full control over the intensity of the light in 1/3 stop increments from full power all the way down to 1/128 power.
Canon 5D Mark II: I used this camera exclusively for a little over a year and it's now my back-up camera. It's still an absolute powerhouse though so if you can pick up a second-hand one for under $1200 I'd highly recommend it! Since Magic Lantern (http://www.magiclantern.fm/) isn't yet compatible with the 6D, I still use the 5D often for video. One of its major drawbacks however is that it is unable to shoot at 60fps, so slow-motion capture is out of the question.