How widely used are 印章 compared to signatures?
Organizations often use 印章 while signatures are used personally.
If you are representing an organization, 印章 usually are required, but signature is acceptable for a person representing himself. 
Example:
A bank is providing a loan to me, on the contract there will be bank employee's signature, bank's 印章 and my signature, this is acceptable.
Of course, if you have a personal 印章, you can use it with your signature, that's fine.
PS: This is in mainland China, not sure the what the situation is in Taiwan