Wow, I'm surprised to hear such hard-line answers as to whether parents should co-sign for their kids. Mine would be "it depends." By the time a kid is 18, his parents should have had many opportunities to observe his work ethic and how responsible he is relative to money management. Did he demonstrate a desire to earn money through work? If so, did he spend it, save it, or some of both and in what proportion? Did he show up to work regularly and on time?
If they are responsible with money and have a good work ethic, they won't need
you to co-sign a loan (or lease) for them. In fact, by not co-signing you're affirming their responsibility and letting them "grow up" normally. By co-signing you're signalling that you think they are still a child and can't be trusted on their own.
On the other hand, if they are irresponsible and therefore "need" you to co-sign then you'll probably just end up with less money and an adult child that will both depend on you and resent you.
My last apartment required a cosigner since I'd been living at my parents and had no recent rental history. At the end of the 6 month lease - the longest they allow for new renters - they let me sign my next lease on my own. I'd been living at my parents because of health issues, not irresponsibility.
Since my mom agreed to cosign for me I was able to move out of the house, pay my own rent, and develop more independence from my parents. My mom only agreed because I had a stable, reliable job and she knew that I'm responsible enough to pay my bills on time.