Short answer: it depends.
It will depend on what you need. In general, if you don't need a lot of info from the user, it's a good idea to keep it all compact and in one page.
There can be a lot of exceptions, not only based on length, but also conceptual exceptions.
Think of this: an user is the sum of many different parts, needs, craves, goals, experiences and so on. So it's easy to see it's impossible to give a "one size fits all" answer. This being said, you won't need all of those parts in a simple profile, but depending on context and needs, you might need different information.
The most important questions are: what is this for? why do I need X info?
For example, it's not the same to ask to fill a Facebook profile than asking for information for medical records, or financial apps, or an ERP. There are many different dimensions of information for these different scenarios.
With this being said, it's not a good idea to mix public and sensitive information on the same page. Instead, you can create a "Profile" section/taxonomy with different sub-sections. For example: Personal Info, Financial Info, Personal settings.
Another thing to consider: unless information is too short, it's a good idea to differentiate static information from user actions and abilities. See below:
Of course, these aren't the only possibilities, but hope this will give you an idea.
As you may see, there are many many different possibilities, the important part
is to make sure the info you request is REALLY needed and that you don't annoy your user with unnecessary info requests, specially if the user may perceive it will be used for an invasion of her privacy, spam, etc