Why does .NET use int instead of uint in certain classes?

I always come across code that uses int for things like .Count, etc, even in the framework classes, instead of uint.

What's the reason for this?

UInt32 is not CLS compliant so it might not be available in all languages that target the Common Language Specification. Int32 is CLS compliant and therefore is guaranteed to exist in all languages.

int, in c, is specifically defined to be the default integer type of the processor, and is therefore held to be the fastest for general numeric operations.

Unsigned types only behave like whole numbers if the sum or product of a signed and unsigned value will be a signed type large enough to hold either operand, and if the difference between two unsigned values is a signed value large enough to hold any result. Thus, code which makes significant use of UInt32 will frequently need to compute values as Int64. Operations on signed integer types may fail to operate like whole numbers when the operands are overly large, but they'll behave sensibly when operands are small. Operations on unpromoted arguments of unsigned types pose problems even when operands are small. Given UInt32 x; for example, the inequality x-1 < x will fail for x==0 if the result type is UInt32, and the inequality x<=0 || x-1>=0 will fail for large x values if the result type is Int32. Only if the operation is performed on type Int64 can both inequalities be upheld.

While it is sometimes useful to define unsigned-type behavior in ways that differ from whole-number arithmetic, values which represent things like counts should generally use types that will behave like whole numbers--something unsigned types generally don't do unless they're smaller than the basic integer type.