Here is a list of some popular free calling applications in no particular order
Skype was perhaps the pioneer in this space and continues to be used by a large number of people. The app lets you do text, voice and video chats. It also enables users to do group calls and call landlines and mobile phones at a cost.
Tango is another nifty application that lets you make free calls. This app also comes with a "Push-to-Talk" feature, which helps in turning your smartphone into a walkie-talkie.
Fring is also a free application that enables you to make free calls. The group calling feature helps you to talk simultaneously with up to 4 participants. Just like Skype, Fring can also be used to make calls to regular phones around the world at an additional cost.
With the help of Viber, users can make free calls, send free texts and share location and setting. For using Viber, you don't need to create a separate username, as your mobile number doubles up as your ID. After you have installed the Viber app, it syncs your mobile contact list, automatically detecting which contacts area already using Viber, similar to WhatsApp.
Nimbuzz lets you send free messages and call other Nimbuzz users. This app has started offering 'NimbuzzOut' service, which is a low cost Pay-As-You-Go option to make calls to other mobiles and landlines numbers across the World
WhatsApp is perhaps the most well know application in the list, outside of Skype, and has become the proffered alternate to SMS for millions across the globe.
Hike is a desi app that offers a feature-set very similar to WhatsApp, though it offers additional features like sending SMS to non-Hike users, walkie-talkie mode and more.
Line is another popular app that offers features similar to those in the list, including voice chat, stickers, and more.
Bonus: Facebook Messenger
If you spend all day on Facebook, you don't need to look beyond Facebook Messenger.