Ideally you will need a broadband connection with a speed of at least 128 kbps (like ADSL or Fibre Optic) to ensure good call quality and successfully use VoIP. There are various reasons for this.
1. You need at least 64 kbps download plus 64 kbps upload bandwidth per call. If you notice a drop in call quality, you can use compression codecs such as G.729 which can decrease the bandwidth to approximately 30 kbps. However such methods of compression are usually used in situation when multiple calls are going over the same connection.
2. A reliable broadband connection with no packet loss or delay, thereby ensuring that you can receive and make calls with minimum interruption.
3. Depending on how you use your Internet connection, you want to make sure that you have enough bandwidth left over for typical Internet traffic (e.g. emails, web browsing, file downloads).