I'm fortunate in that my nails are really hard and don't break. They grow as long as I want them to grow, but they are often a pain in the bum because I'm too lazy to cut them at times. I treat them terribly - I open containers with them, bleach them with actual bleach now and then, and play way too much bass in Rock Band - but they won't break. When I fell down the stairs on the ferry last year, everyone was surprised I only chipped one nail and didn't break my pelvis. (Whatever gives you strong hair, bones, and nails - apparently, I got a double dose of it!)
I know, most women would love to have my problem, and I don't think there's some magic remedy to making weak nails stronger, but I have one piece of advice. Don't file them. I never file my nails - okay, if there's a tiny bit where it's catching on fabric I do - but I think it ruins the structural integrity and leads to more breakage. I don't know if this is true, but it seems to work for me.
The other thing I suggest is to keep your hands and nails well moisturized. I like to use a manicure scrub like this one (link to body and manicure scrub in a previous post). I found on the road trip that my nails were almost peeling they were so dry. A little lotion and tons of manicure scrub in the last three days have helped this problem.
You'd think I'd be obsessed with nail polish, but I'm not. I rarely find colours I like...but thanks to Anne-Marie at the Soap Queen - that problem's solved!