I guess it depends on circumstances, and what you can/can't afford to do for your adult kids. To my detriment, I've always been a bit of a soft touch (and my husband to a certain extent), but there does come a time when it needs to stop ...
When we go out for meals, we always pay and, as it's something we've always done, I guess our kids have grown to expect it. My DS & DiL would never think to put their hands in their pocket, yet my DD and her partner often offer to pay, although we don't let them, as it wouldn't be fair, but we do appreciate the offer!
DD & her partner, don't earn a great deal, but they do have their own home, and they both budget remarkably well, and manage to go on nice holidays. DD rarely asks for any financial help, and even then, only in an emergency if she needs to.
DS & DiL, on the other hand, have been a constant drain on us! They both have relatively decent jobs, but tend to live outside their means, buy things they really can't afford, instead of saving for them first, and due to certain circumstance, they have had a few difficult times. We have helped them out as much as possible, and so have the other in-laws. However, there does come a time when they need to stand on their own feet and be more responsible, especially now that they have a child.
They've been lucky that we've been in a financial position to help them, but once my OH retires, we simply won't have the spare money to keep bailing them out, as we need to make sure we have money to live our own lives!. After the most recent crisis, DiL's mum came to me to discuss how we were going to help them. Frankly, I told her that this time they needed to sort it out themselves, as I don't think we are doing them any favours constantly bailing them out. I also spoke frankly to my DS about the situation, who agrees that they need to sort themselves out once and for all ... but guess what? ... other in-laws bailed them out anyway (supposedly for the last time!), but still makes us look like meanies!
Obviously, in any emergency situations, we would always help out either of our kids. But we've done our bit for now, and it's time for them to start taking responsibility for their own finances ... We have a retirement fund that needs building up!!