C# Should I Loop until no exception?

This smells of bad design to me. The general rule is: exceptions should not be used for flow control. There are a number of reasons for this; namely, there are usually better/more reliable methods that can be used to check things before an exceptions is thrown, and also it decreases efficiency.

Nonetheless, just for the sake of argument, you could do something like the following:

while (true)
{
    try
    {
        // do stuff here
    }
    catch (MyException)
    {
        continue;
    }

    // all is good
    break;
}

Again - this is not the recommended way. I would be happy to suggest something better if you could provide a bit more context/examples/

What about the following where you can set a retry count:

            int tryCount = 0;

            while (tryCount < 3)
            {
                try
                {
                    someReturn = SomeFunction(someParams);
                }
                catch (Exception)
                {
                    tryCount++; 
                    continue;
                }
                break; 
            }

That really depends on what you're doing, and the type of exception being thrown. Many exceptions aren't something that would be fixed by just trying again with the exact same inputs/data, and thus looping would just keep generating the exception ad infinitum.

Instead, you should check for relevant exceptions and then handle them in an appropriate manner for those particular exceptions.