Tywan Terrell has a listing of various functions built into SQL Server:
SQL Server starting with 2012 ship with a robust set of functions that can be used to make code perform faster, with fewer lines of code. The functions can be used in ETL Process to provide better error handling. A example of this would be the Try_Parse function that allows you to check if a value can be converted.
Another example would be using the FIRST_VALUE() and LAST_VALUE() functions which work against a set of data. These functions are very useful when looking for things like month over month averages and when doing calculations. The table below contain a list of function that are supported starting with 2012 along with some examples of how to use them.
He breaks them down into four categories and provides examples. Functions can bring their own set of problems with query performance, but most of them can be very useful.