The answer depends on so much that it may be difficult to fully represent the issue in a single article.
However, there are some broad aspects that are worthy of your consideration.
Cats vomit up anything that remotely upsets their stomach.
This can be a very healthy way of remaining healthy, or a sign to let you know all is not well.
Lets first look at those areas not to worry about.
All cats vomit up hairballs when their coats change according to the season.
So early spring and autumn will always be a time of increased vomiting up hair balls.
This is entirely natural, normal and should not be interfered with.
Sometimes food will be vomited up with the hairball.
The timing of the meal was not perfect.
The hairball needed to come out, so regardless of what else is in the stomach, out it comes.
Again, this is entirely normal and natural and should never be interfered with.
A long haired cat who is not groomed often, will obviously have more hair balls than a short haired cat.
A cat with free access to grass will occasionally vomit up the grass with a little saliva.
This has a natural cleansing function and is no cause for alarm.
Whilst it may be messy, having a cat vomit indoors, it's part of having a cat in your life.
It's best to take the 'bad' parts along with the good.
Now let's examine times when a cat vomiting indicates a cause for concern.
Frequent vomiting, such as minutes, hours, even days does indicate a deeper problem.
Food can be purged back up when the quality is not good or when your cat is feeling below par.
Vomiting can indicate an acute problem with food poisoning or a serious or chronic problem with the liver or stomach.
Although this may require professional help, the first thing to consider is what went before this.
That is often the key to the problem.
Reverse this, if you can, and the problem may disappear.
However, some health issues can develop slowly, over time making isolating the cause more tricky.
In many situations, you can stop the vomiting altogether by changing the diet of your cat to a natural one.
Even when the condition is serious, even life-threatening, a natural diet can make the difference to bringing hope to an otherwise hopeless situation.
Many cats make a miraculous recovery, even from apparently impending death, simply by switching the diet to a natural one.
It's always worth trying, as you'll otherwise never know.