If you\\\'re using .NET 3.5 you can do this in a one-liner with LINQ:
int count = source.Count(f => f ==\\\'/\\\');
If you don\\\'t want to use LINQ you can do it with:
int count = source.Split(\\\'/\\\').Length-1;
You might be surprised to learn that your original technique seems to be about 30% faster than either of these! I\\\'ve just done a quick benchmark with \\\"/once/upon/a/time/\\\" and the results are as follows:
Your original = 12s
source.Count = 19s
source.Split = 17s
foreach (from bobwienholt\\\'s answer) = 10s