A few of the most popular online chat services are Skype, Discord and IRC. These all offer different types of services that are used by different people in different situations.
Skype provides a very wide array of features that customers usually look for in a chat service, allowing users to create persistent profiles and thus be able to maintain lists of contacts that they can chat with at any time. Skype offers text, voice, and video chats, and even allows all to be used in a group setting, where one can create persistent rooms that all contacts involved will receive messages for. Skype is even available on mobile, and it offers services that allow a person to call out to normal phone numbers and receive them as if it were a normal phone as well.
Discord is a newer service that is trying to provide services similar to Teamspeak and Ventrilo. Discord focuses more on the persistent chat room aspect of chat services but also has voice chat. It is unique in that one does not have to start a call or be forced into a voice chat room for these services, they may merely join in whenever and wherever they please. The service's app is very user friendly, and is currently actively being updated and improved upon with new features by the developers.
IRC is a relic of the past in terms of the Internet, but it is still used by the technically savvy. While not very user-friendly, certain communities like to use Internet Relay Chat for communication. This is only a text chat, and uses a sometimes spotty connection protocol, but its versatility (if the users know what they're doing) for more than just chatting has kept this type of chat alive since 1988.