Granted, I haven't owned one, but I do more than browse the internet. Netbooks typically can't provide enough horsepower to run all of the programs I like to run at the same time.
What sorts of stuff are you running? My experience with high-end notebooks these days is that they can run basically anything -- fairly high end games, as many desktop apps as you can download, even Matlab runs pretty well on my laptop. So long as you aren't hosting a serious website or doing some crazy data analytics AI stuff, I think you're fine.
The main problem is the screen real estate and keyboard size. I just can't type at speed on the eee, I keep hitting all the wrong keys and it gets very frustrating. It's fine for the odd email, but no way could I crank out the code on it. The screen is also too small. My main laptop has a nice widescreen where I typically have 2/3rds IDE and 1/3rd documentation/consoles. Not possible on 7-8" screens.
It works great with the new "cloud" web apps like dropbox and google docs offline.