I am specifically thinking about unsigned int.
Here is a practical example: what do you do when your identity column maxes out? It's possible to either go BigInt (8 bytes storage instead of 4) or to refactor the application to support negative integers, and even to create your own rules as indicated in this answer; neither of those options are optimal.
UInt would be an ideal solution, but SQL Server does not offer it (where MySQL does).
I understand that unsigned datatypes are not part of the SQL standard (SQL-2003) but still seems like a waste to me.
What is the reason of not including these (in SQL Server or in the standard)?
If I had to guess, I would say that they are trying to avoid a proliferation of types. Generally speaking there isn't anything that an unsigned integer can do that a signed integer can't do. As for the case when you need a number between 2147483648 and 4294967296 you probably should go to an 8 byte integer since the number will also eventually exceed 4294967296.