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Binary Tree is one of the most used Tree Data Structure and is used in real life Software systems.
Following are the Applications of Binary Tree:
 Binary Tree is used to as the basic data structure in Microsoft Excel and spreadsheets in usual.
 Binary Tree is used to implement indexing of Segmented Database.
 Splay Tree (Binary Tree variant) is used in implemented efficient cache is hardware and software systems.
 Binary Space Partition Trees are used in Computer Graphics, Back face Culling, Collision detection, Ray Tracing and algorithms in rendering game graphics.
 Syntax Tree (Binary Tree with nodes as operations) are used to compute arithmetic expressions in compilers like GCC, AOCL and others.
 Binary Heap (Binary Tree variant of Heap) is used to implement Priority Queue efficiently which in turn is used in Heap Sort Algorithm.
 Binary Search Tree is used to search elements efficiently and used as a collision handling technique in Hash Map implementations.
 Balanced Binary Search Tree is used to represent memory to enable fast memory allocation.
 Huffman Tree (Binary Tree variant) is used internally in a Greedy Algorithm for Data Compression known as Huffman Encoding and Decoding.
 Merkle Tree/ Hash Tree (Binary Tree variant) is used in Blockchain implementations and p2p programs requiring signatures.
 Binary Tries (Tries with 2 child) is used to represent a routing data which vacillate efficient traversal.
 Morse code is used to encode data and uses a Binary Tree in its representation.
 Goldreich, Goldwasser and Micali (GGM) Tree (Binary Tree variant) is used compute pseudorandom functions using an arbitrary pseudorandom generator.
 Scapegoat tree (a selfbalancing Binary Search Tree) is used in implementing PaulCarole games to model a faulty search process.
 Treap (radomized Binary Search Tree)
Why is Binary Tree is so widely used?
Binary Tree is the most widely used Data Structure because:

Binary Tree is the most simpliest and efficient data structure to be used in most Software Systems. It is the properties of Binary Tree that makes it so widely used.

Nary Tree which is the generalization of Binary Tree is complex to implement and is rarely a better fit.

Binary Tree can be implemented as an array using ideas of Binary Heap. Hence, the ideas of OOP (Object Oriented Programming) is not necessary for a safe implementation.

There is a wide range of variants of Binary Tree which makes it very likely to find a suitable variant for a specific problem. For example, if we want a Data Structure where recently accessed elements are closer to the beginning of the data structure so that access is fast, then we have a variant of Binary Tree known as Splay Tree.
Alternatives to Binary Tree
Despite the wide use of Binary Tree, there are a few Data Structures that have found strong use case and Binary Tree cannot replace them in terms of performance.
Alternatives to Binary Trees are:
 BTree and B+ Tree: used in indexing of database
 Space Partitioning Tree: For higher dimensional games
 Quadtree
 Tree pyramid (Tpyramid)
 Octree
 kd (K dimensional) tree
 Rtree: to find shortest path or nearby objects in 3D graphs
With this, you must have the complete idea of where Binary Tree is used in real life Software Systems. Keep an open mind and use other Tree Data Structures when needed.