How do I check "no exception occurred" in my MSTest unit test?

In NUnit, you can use:

Assert.DoesNotThrow(<expression>); 

to assert that your code does not throw an exception. Although the test would fail if an exception is thrown even if there was no Assert around it, the value of this approach is that you can then distinguish between unmet expectations and bugs in your tests, and you have the option of adding a custom message that will be displayed in your test output. A well-worded test output can help you locate errors in your code that have caused a test to fail.

I think it's valid to add tests to ensure that your code is not throwing exceptions; for example, imagine you are validating input and need to convert an incoming string to a long. There may be occasions when the string is null, and this is acceptable, so you want to ensure that the string conversion does not throw an exception. There will therefore be code to handle this occasion, and if you haven't written a test for it you will be missing coverage around an important piece of logic.

Your unit test will fail anyway if an exception is thrown - you don't need to put in a special assert.

This is one of the few scenarios where you will see unit tests with no assertions at all - the test will implicitly fail if an exception is raised.

However, if you really did want to write an assertion for this - perhaps to be able to catch the exception and report "expected no exception but got this...", you can do this:

[Test]
public void TestNoExceptionIsThrownByMethodUnderTest()
{
    var myObject = new MyObject();

    try
    {
        myObject.MethodUnderTest();
    }
    catch (Exception ex)
    {
        Assert.Fail("Expected no exception, but got: " + ex.Message);
    }
}

(the above is an example for NUnit, but the same holds true for MSTest)