Why .NET String is immutable?

Making strings immutable has many advantages. It provides automatic thread safety, and makes strings behave like an intrinsic type in a simple, effective manner. It also allows for extra efficiencies at runtime (such as allowing effective string interning to reduce resource usage), and has huge security advantages, since it's impossible for an third party API call to change your strings.

StringBuilder was added in order to address the one major disadvantage of immutable strings - runtime construction of immutable types causes a lot of GC pressure and is inherently slow. By making an explicit, mutable class to handle this, this issue is addressed without adding unneeded complication to the string class.

1. Instances of immutable types are inherently thread-safe, since no thread can modify it, the risk of a thread modifying it in a way that interferes with another is removed (the reference itself is a different matter).
2. Similarly, the fact that aliasing can't produce changes (if x and y both refer to the same object a change to x entails a change to y) allows for considerable compiler optimisations.
3. Memory-saving optimisations are also possible. Interning and atomising being the most obvious examples, though we can do other versions of the same principle. I once produced a memory saving of about half a GB by comparing immutable objects and replacing references to duplicates so that they all pointed to the same instance (time-consuming, but a minute's extra start-up to save a massive amount of memory was a performance win in the case in question). With mutable objects that can't be done.
4. No side-effects can come from passing an immutable type as a method to a parameter unless it is out or ref (since that changes the reference, not the object). A programmer therefore knows that if string x = "abc" at the start of a method, and that doesn't change in the body of the method, then x == "abc" at the end of the method.
5. Conceptually, the semantics are more like value types; in particular equality is based on state rather than identity. This means that "abc" == "ab" + "c". While this doesn't require immutability, the fact that a reference to such a string will always equal "abc" throughout its lifetime (which does require immutability) makes uses as keys where maintaining equality to previous values is vital, much easier to ensure correctness of (strings are indeed commonly used as keys).
6. Conceptually, it can make more sense to be immutable. If we add a month onto Christmas, we haven't changed Christmas, we have produced a new date in late January. It makes sense therefore that Christmas.AddMonths(1) produces a new DateTime rather than changing a mutable one. (Another example, if I as a mutable object change my name, what has changed is which name I am using, "Jon" remains immutable and other Jons will be unaffected.
7. Copying is fast and simple, to create a clone just return this. Since the copy can't be changed anyway, pretending something is its own copy is safe.
8. [Edit, I'd forgotten this one]. Internal state can be safely shared between objects. For example, if you were implementing list which was backed by an array, a start index and a count, then the most expensive part of creating a sub-range would be copying the objects. However, if it was immutable then the sub-range object could reference the same array, with only the start index and count having to change, with a very considerable change to construction time.

In all, for objects which don't have undergoing change as part of their purpose, there can be many advantages in being immutable. The main disadvantage is in requiring extra constructions, though even here it's often overstated (remember, you have to do several appends before StringBuilder becomes more efficient than the equivalent series of concatenations, with their inherent construction).

It would be a disadvantage if mutability was part of the purpose of an object (who'd want to be modeled by an Employee object whose salary could never ever change) though sometimes even then it can be useful (in a many web and other stateless applications, code doing read operations is separate from that doing updates, and using different objects may be natural - I wouldn't make an object immutable and then force that pattern, but if I already had that pattern I might make my "read" objects immutable for the performance and correctness-guarantee gain).

Copy-on-write is a middle ground. Here the "real" class holds a reference to a "state" class. State classes are shared on copy operations, but if you change the state, a new copy of the state class is created. This is more often used with C++ than C#, which is why it's std:string enjoys some, but not all, of the advantages of immutable types, while remaining mutable.