The DSi works great.
The batterylife is ok, if you leave the wifi enabled you can still play with it for about 4 hours.
I downloaded "Asphalt 4: Elite Racing" from the DSi ware shop. (You get a 1000 points if you register the DSi) The speed of the game is much better then comparable games for the DS. The faster CPU is for sure an improvement.
If you use regular DS games the CPU will run on the old DS speed.
The browser is OK, it is the opera browser like in the archos and wii. The loading of big pages can be a bit long, but for checking mail it works really well. Unfortunatly no flash support.
The webcams are nice to play with, but with 0.3 Megapixel it is a step back. For the small screens on the DSi it is however good enough.
Hopefully the homebrew scene (don't confuse this with piracy ) will take off. There is already some progress from the guys who hacked the Wii for installing a homebrew channel on that. Take a look here
http://hackmii.com/2009/07/dsi-mode-homebrew-anyone/ Offcourse these are only the first steps and it will take a long time before there is anything like a homebrew channel for the DSi. For the Wii it almost took 3 years.
Maurice
If the last lines are against the forum rules, please tell me and I edit them out.