I need to let end users specify a time range, to be stored and used internally as a starting date/time and ending date/time. The range could be minutes or it could be days.
User interface design is heavily application dependent. "Best" implies some kind of metric that can measure solutions. In UI design such a metric can be "home many clicks/key-presses does it take to complete the task?" where a smaller number is better. So once you've defined your metric you can start to sort solutions into good, better and best.
You also want to reduce cognitive burden for the user. If the user has to enter the final day on which a product can be exchanged based on a 90-day return policy then asking for start and end date would force them to do date math which is no fun. In this example a start date with a "delta" of x days would place less of a burden on the user.
Depending on you application you could consider and approach like the Google Finance time range selector on their charts: http://finance.google.com/finance?q=.dji