No,You can't use your T-Mobile phone with sprint service.Because T-Mobile is GSM,Sprint service is CDMA.
But you will be able to use other GSM carriers.If you are interested to use other GSM carrier on your mobile phone means,Make sure your phone is free from any network lock.If it's locked,you will need to unlock your phone.For unlocking you can approach your service provider or else try to buy an unlocking service from any one of the online unlocking service provider like Unlock-Zone.com Here you can unlock your phone at low cost and you can get free how to enter unlock code instructions from MobileUnlockGuide.com