Why F#? What does F# provide that C#, VB, etc. does not?
1. By default, F# uses immutable types, which means that once a type is created, it will not change. This behavior makes the language inherently safe for concurrent operations. With an ever increasing need for concurrency support in enterprise applications, this behavior is becoming more and more desirable. With F#, concurrency related errors such as race conditions, synchronization issues, lock convoys, and deadlocks will be greatly reduced.
2. F# is built on the concept of functions rather than objects. While objects are supported, functions are also first class citizens. Functions can be and passed around like objects in C#/VB. This makes the language extremely well suited for algorithmic computations and makes it easier to achieve efficient processing of lists of data. Since everything compiles to IL, similar performance on these operations could conceivably be achieved with any .NET language, but F# allows optimal performance for specific operations with much less code. Note: In addition to the new abilities, you still have all functionality available in the .NET framework.
3. One of the features of F#, that I have found extremely useful, is the interactive scripting functionality. This allows the developer to select a subset of code and run it like a script. Anyone with a background it SQL will find this functionality very easy to understand and extremely useful for learning/experimenting with the language.
4. Finally, anyone with experience in C# will be thrilled to learn that the immutable aspects of F# will greatly reduce or eliminate the dreaded "Object reference not set to an instance of an object" error.
Note: F# should be added as an addition to an engineer's arsenal, not a replacement for the existing language of choice. My philosophy has always been, use the tool that is best suited for the task. Use F# in places where it can accomplish the task better and/or easier than the other available options.
Many of the points listed here are based on comments/documentation from the following:
Ted Neward: (http://msdn.microsoft.com/en-us/magazine/cc164244.aspx,
The book "Expert F#" (http://search.barnesandnoble.com/booksearch/isbnInquiry.asp?isbn=1590598504)