The short answer is..yes! You will need to pass a basic credit check with each carrier if you want to spread the cost of a new phone using monthly installment plans.
The reason for this, lets say you want a new iPhone - if you go to an Apple store and buy a new phone they will ask you for $600-700. The same phone that one of the carriers are offering for $25 a month still cost the carrier $600-700...they have to make sure that you will be able to pay for the phone and have a good credit history.
Each carrier will have different approaches to credit checks, some will be really tough to pass and are all dependent upon what value the phone is, how long the finance term is etc.
If you have fair to good credit scores then you should be fine
If you have a lower credit score it may be better to look for a lower priced phone and buy it outright - you can get some great phones for less than $200