Google Voice (www.google.com/voice) is an online phone service that inter-connects with your Chrome account and your Gmail.
You can choose a phone number (from a provided list); if someone leaves you a voicemail at that number, you can set Voice to set an audio file of the voicemail to your Gmail, which you can play right in your Gmail.
Voice will also send you a typed-out transcript of the voicemail (subject to translation errors).
The initial set-up requires you to have a phone number (like a cell phone) to link Voice to. Calls can be forwarded from your Voice number to the set-up number, which allows you to set up a number people can call without having to give out your "regular" phone number (Once you have set up Voice, you can delete the "set-up" number).
You can also use Voice to send text messages and make phone calls within the U.S. for free.