Skype
Skype has been around since the very early days of video calling, and it's pretty much synonymous with staying in touch with faraway friends and family. It's mostly known for video calling, but you can make audio/voice-only calls using Skype on your mobile device and computer, too.
Google Hangouts
Hangouts was originally an app for Google's desktop Gmail chat feature (also now called Hangouts), but it has evolved to include voice and video calls on both mobile devices and computers.
FaceTime Audio (iPhone only)
Like Skype, the iPhone's FaceTime app is mostly known for video calls, but it can be used for audio/voice calls, too.
It's for iPhone and Mac only, but if you know your friends or family have iPhones, then you know they have the FaceTime app.
WhatsApp
WhatsApp is an international favorite for messaging, and it can make better phone calls than your regular phone app.
Unfortunately, it doesn't have video calling, and you can't make calls from your computer.