If you already have a GSM mobile phone, you can bring it with you and use it in Romania. In some cases you may need to get your phone ‘unlocked’ from the network in your home country (this can be done cheaply at most mobile phone shops). If you have a CDMA phone (many US users and some Asian users), you may be able to use it in Romania, but probably only with Zapp.
You can buy a new SIM card with number for a reasonable price and will be able to call or send SMSs worldwide. It is useful to know that almost all mobile telephone companies also offer internet services and some now offer fixed-line telephony as well.
All of the main providers have some information in English: