Q:

SQL counter variable @Count += 1

I would like to know if it's possible to create a Count variable like you would in C#.
DECLARE @Count Int
SET @Count = 0

--something happens
SET @Count += 1

--something happens
SET @Count += 1

IF @Count < 3
BEGIN
--Do something
END

A:

In SQL-Server you can do It in following:
SET @count = @count + 1

A:

In SQL Server 2008+ your code is perfectly valid:
DECLARE @Count INT;
SET @Count = 0;

PRINT @Count;
SET @Count += 1;

PRINT @Count;
SET @Count += 1;

IF @Count < 3
BEGIN
  PRINT @Count;
END

LiveDemo
With version before 2008 you can use full syntax:
SET @Count = @Count + 1;

+= operator

Adds two numbers and sets a value to the result of the operation. For
  example, if a variable @x equals 35, then @x += 2 takes the original
  value of @x, add 2 and sets @x to that new value (37).

