I have a spreadsheet in Google Docs. Users can change everything and anything in the spreadsheet.
Now, I want them to be able to change empty fields or their own fields only.
Is this possible? If yes, how?
It's not possible using just Google Docs. If you've written some sort of program that just uses Google Docs as a storage mechanism, then you can do anything you want. For example, you could add a column that records the name of the person who created each row. When someone tries to edit a row, verify that they are the person listed as the row creator before accepting the edit.
Google spreadsheets can't do this. I don't think they've said that they'll implement it, either. I'm not sure what your exact situation is, but if you have a small, known number of users, you might try:
If your number of users is large or might grow faster than you care to manually add private spreadsheets, this obviously won't work. If that's the case, you might have to look elsewhere for a solution. I'm pretty sure the Office Web Apps would solve your problem, but those aren't free.