Very customizable with a lot of clean looking options.

In addition to the end-to-end encryption that provides privacy to communications, the app also includes self-destructing timers for chats, and the ability to permanently delete messages, yours and theirs, from your device.

You can post voice and video messages if you are too lazy to write text messages.

Works on Windows, Mac, Linux, Android iOS, Windows Phone, and Firefox OS even. Has a web app that changes it's appearance based on the device it's running on and if it's browser is full screen, etc.

You can ping people to get their attention by @mentioning them.

There are native desktop, mobile and web client apps, that are optimized for speed and are light on memory usage.

Client apps are open source, making whole service more trustworthy.

Even though encryption used for cloud based storage (e.g. Gmail, Facebook, iCloud) may not be as secure as end-to-end encryption or zero-knowledge storage, Telegram does the most that it can by holding keys to chats in different jurisdictions, requiring intergovernmental cooperation to obtain the keys. This is aside from whatever security measure are taken place, of course.

You can pin messages to the top of groups or supergroups so members will see them when opening the group.

Unlimited number of files can be stored forever on the cloud. You can upload files up to 1.5 GB each.

The application is available free of cost.

Telegram uses an open source MTProto encryption protocol that provides complete end-to-end encryption for secret chats. To show off their confidence in the protocol the company behind Telegram has organized $200,000 and $300,000 challenges to break the encryption. So far there have been no winners.

Videos, gifs, images, geolocation, and documents.

You can set up an additional password to your account, which can be reset by your email. You don't have to use an email, if you do not want to. If you lose access to your email or forget your password, you will be able to reset if via text message if you're account is over seven days old and will receive it within a week (in case you recover anything before then).

Unfortunately, on the desktop, videos don't apply, but images are viewable without visiting popular websites like imgur and Instagram.

You can play YouTube videos and others within the app, so you don't need the embed code or anything.
With inline bots, such as @gif, @pic/bing, @vid/YouTube, etc, you can look things up without leaving the client or chat that you're in. Simply type the name and some keywords and wait for the results to load.

Copy/paste videos, gifs, images, geolocation, and documents, drag over files for practically any time up to 1.5GB in size. Images can be compressed, too.

Broadcasting channels suitable for announcing things.

In Supergroups, anyone along with admins can delete their messages from all sides. A message can be pinned to the top. All of the user's messages can be deleted by an administrator, and they can be banned and reported as well. Supergroups can have a public link (outside of Asia, due to high spam volumes), which is also a username.

Even though encryption used for cloud-based storage (e.g. Gmail, Facebook, iCloud) may not be as secure as end-to-end encryption or zero-knowledge storage, Telegram does the most that it can by holding keys to chats in different jurisdictions, requiring intergovernmental cooperation to obtain the keys. This is aside from whatever other security measures have been taken, of course.

Messages can be set on a timer. They will disappear after the timer expires.

This Discord-like feature adds to the interactivity of the application.

Although it's volunteer-based, still pretty top-notch if available, which it tends to be.

The desktop app has a built in setting to scale the UI of the app up to 200% which allows for those with 4k monitors/screens to use the app without scaling issues.