Yes, each new plan (account) does require a credit check.
If you simply have no credit, chances are pretty good that you'll be able to start with little or no deposit. You may have a Account Spending Limit, which is just a maximum your bill can be each month. You may also have to set up automatic payments or be charged a small monthly fee.
If you have troubled credit, there may be a deposit required in addition to the Spending Limit. Sprint is very good in working with customers who want to establish or re-establish credit.
Barring that, Virgin Mobile and Boost Mobile also offer some outstanding deals on phones and service, with no credit check.