From everything I've been told, HP is a pretty decent, affordable brand. I wouldn't go with Dell though. Myself included, everyone I know who's had one wound up with problems within the first year.
I have had a Dell Inspiron 2200 for a bit more than 5 years and never had trouble with it.
I like it. It really depends on what you want a laptop for. I pretty much only use my laptop for research, browsing the internet, watching videos, and typing up papers. It's pretty good for all that non-fancy foofoo stuff.
The main cons that I see with this computer are the facts that:
It gets a bit too warm for my tastes. I know laptops tend to get warm when used a lot, but this one, although fine, tends to be a bit warmer.
The battery chargers get messed up enough. This is the only part of the computer that I've had trouble with. The battery chargers tended to get short-circuited and shorted out on me. No, this did not mean fire lol. It just meant the chargers needed to be replaced XD.
I have replaced the hard drive on here just because when I bought it, it was big for the time, but I needed more space.
It's really just their laptops I dislike. My mother has had a Dell desktop for well over 5 years and she's not had any problems with it (aside from the occasional virus thanks to my siblings, paired with crappy anti-virus software).
I wouldn't rely on JUST the opinions you get on here, though. Go around to places that sell computers (ideally somewhere like Circuit City, rather than Wal-Mart) and ask them for further advice.
I got a Dell a year ago, and so far my hard drive has crashed, my keys are loose, and my screen a bit wobbly. I wouldn't go with a Dell even though I still love mine :3

Macbook. The best computer(s) on the market to date. I dislike Windows Vista, so it's another plus for me. :) Macs are more compatible, better for creative stuff, and run Microsoft Office. They also (if you have to) run Windows alongside Mac OS X.
Silence is golden... Duct tape is silver.
I dislike Dell. I've owned one for a good, say, three years or so? It had a LOT of problems. Shut down on me one day, had a horribly blue screen. :(
That's when my dad got me a Toshiba.
It has 250GB AND a webcam.
I love it so <333
It's good for viewing videos and browsing internet (though it depends on the Internet provider... I have Comcast and sporadically, I'll randomly get disconnected so I have to reconnect. T.T)
Gah. That fucking blue screen of DEATH. I hate it so very much.
If you're getting a laptop that runs windows, I'd wait until Windows 7 is default on laptops because it's so much better than Vista.
I've also heard (from a few computer-savvy people) that Vista isn't nearly as bad as everyone makes it out to be. I've not tried Vista myself, though. My laptop came with XP, and my fiance paid extra for XP (he did get a backup disc for XP AND Vista with his laptop though).