SIM cards are essentially universal and interchangeable; any SIM card will fit into any cell phone. However, if you're changing service, you'll need to ensure that your phone is unlocked by the provider before you can use a different company's card in it.
No assuming you're talking about the Samsung SCH-i730 by Verizon. That particular phone uses CDMA technology vs GSM. Phones that use GSM work with SIM cards. CDMA phones such as the i730 have your account info built inside the phone so when you change phones, the old one is discarded and the new one activated.