Should I make a DateRange object?

In .NET 4.0 or higher the Tuple<> type was added to handle multiple values.

With the tuple type you can define your own combination of values on the fly. Your problem is very common and is similar to when a function wants to return multiple values. Previously you had to use out variables or create a new class just for the function's response.

Tuple<DateTime, DateTime> dateRange =
    new Tuple<DateTime, DateTime>(DateTime.Today, DateTime.Now);

Whichever route you take, I think you are definitely taking the correct approach. You are giving real meaning to what two dates paired together are. That's self-documenting code and in the greatest way, right in the structure of the code.

No, you didn't miss a general purpose class.

I have a Range type in MiscUtil which you may be interested in - and it certainly makes for simple DateTime manipulation. Referring to Marc's answer, I can't remember whether this is a struct or a class - you'd be welcome to change it of course.

It's nice and easy to step through, due to Marc's generics shenanigans (assuming you're using .NET 3.5, at least - it's feasible with 2.0 but not supported at the moment);

Range<DateTime> range = 19.June(1976).To(DateTime.Today);

foreach (DateTime date in range.Step(1.Days())
{
    // I was alive in this day
}

(That's also using a bunch of extension methods - more useful for test than production.)

To address the other point in Marc's answer, Noda Time will certainly be able to express the concept of a date more appropriately than the .NET API, but we don't have anything like a range at the moment... It's a nice idea though - I've added a feature request.