It's smaller, has more ports, runs quieter and costs the same: $300. It has a 250GB hard drive and built-in 802.11n Wi-Fi. They're shipping the new Xbox 360 to retailers today.
(They're sending out one for free to everyone here, supposedly).
Update: Here are some detailed specs. One of the most interesting details is that this new system has been in development for, give-or-take, two years.
• Touch sensitive on/off and eject buttons (like the PS3)
• "Much quieter"
• 250GB internal hard drive, which is still swappable.
• A custom Kinect port (not a standard USB port—it's a USB port that can feed more power)
• There are five USB ports now, with three in the back and two in the front
• AV cable included, an HDMI and optical audio
• Different power supply—it's still big but nearly weightless
• External Xbox 360 hard drives and memory units are NOT compatible with the new Xbox
• Other accessories are
• Internal components that are changed: two small fans changed into one large fan for quieter operation, 45nm integrated CPU and GPU
Update 2: Some more new details:
The controller is slightly changed, with a chrome Xbox button, the Xbox logo on the back, and squared off shoulder buttons, which don't change gameplay but give it a more angular aesthetic feel. The angularity is also evident in the Xbox 360 itself, which Microsoft said that they updated to match the look of modern AV equipment, which are usually black and glossy and chrome.
To transfer your hard drive from your old console, you can either use a standard old 16GB USB drive and do it chunk by chunk, or you can use the old hard drive transfer cable (it works with the new internal hard drive). Also, you can now purchase that cable separately for $20, if you can find one to bum off of from your friends.
As for the hard drive, it's easily removable and is quite small—much smaller than the current external lump hard drive. You can't use this with older Xbox 360s, and you can't use older Xbox 360s' hard drives with this.
There is a Kinect-specific connector in the back, in addition to the 3 standard USB2 ports already there. The Kinect connector is just a USB port with more power, so you don't need a separate power supply like you would if you used Kinect with an older Xbox 360.
Though this has an HDMI out, the box doesn't come with an HDMI cable. You can pick one up for $5 on Monoprice, of course, but it'd be nice for them to include one. Especially because Sony just decided to included one with their PS3s.
We did turn on the Xbox (touch with audio feedback when you press!), and it sounded very quiet. Almost silent in the somewhat noisy room, but this is just at bootup, with no DVD spinning and nothing really happening. It'll definitely get louder when you play it more, and the DVD will be noisy when that's spinning, but just compared to the bootup on the current Xboxes, it's very quiet.