Quick Impressions: Asus is the innovator and father of the netbook. Its Eee PC excels in almost every respect. There is a reason it is the number one selling netbook, in close competition with Acer's Aspire One. The main reason I love this one so much is their innovation in design and configuration and in the ease of use.
Price Range: $250-$500, probably the cheapest out there without sacrificing much at all.
Availability: Asus offers the full range of netbook configurations--From a low priced 8.9" Linux based PC to a higher end SSD, large battery PC. The coolest thing is, they offer such a huge range that, as long as you get them online (stores will normally only carry one model) you can really customize what you get. If you want a Linux OS with a 9 cell battery and an SSD, I'm sure they have a model for that.
Design and Screen: The Asus features a glossy finish that comes in several colors (black, blue, white, pink) and a build that is thicker in the back and skinnier in the front. The screen is a nice glass with brighter displays than many of the other computers, but this means it does worse if you're trying to use outside since it has a problem with glare. Also just released was the Eee PC Touch, the first netbook with a touch screen.
Ease of Use: This is really where I love Asus. In their newer models (as of Summer 2009) they put in flattened keyboard that I think is the best out there as far as making it easy to type on. Other company's (Dell and HP) put flattened keyboards with keys that sink in slightly in the center for differentiation, but I don't like that much. Also, the slanted design makes for easier typing while it is sitting on flat surfaces. Most importantly, their keypad is the most innovative: it is simply a textured section underneath the keyboard, allowing for a larger surface to navigate with. Also, the touchpad allows you to use multiple fingers, allowing you to zoom in and out using two fingers. Only the Asus and Acers do this, you'd be surprised at how helpful it is while trying to navigate the internet.
Support: Asus doesn't offer the same sort of in-company service that a company like HP or Dell does but they still offer a standard 1-year warranty that I've heard good things about. A friend of mine who had his screen go out sent it off and got it back repaired in less than 2 weeks. Impressive. I've also noticed the company has done a good job going around the Internet and personally responding to any complaints or negative reviews left by customers. That shows some dedication.
For a more in depth review see the in-depth review of the Asus 1000HE.