At one time, there were only a couple of choices for motor oil. Today, that is no longer the case, and hasn't been for quite some time. Here's a quick breakdown of what you need to consider when it's time for an oil change:
Viscosity: Viscosity is how thick your oil is, and how it retains its pour properties at various temperatures. In this respect, synthetic oil is far superior. Conventional oils will thicken in cold weather and thin out when very hot, while the viscosity of synthetic is much more uniform. Check your owner's manual -- many newer models require a thinner, lower-viscosity oil, which also helps the engine run more efficiently. Viscosity is expressed as a numerical value -- the lower the number, the thinner the oil. Many are designed to work at various viscosities, i.e. a rating like 5W-30.
Premium Conventional Oil: For most vehicles, premium conventional oil is just fine. Conventional oil does a good job of protecting engine parts from wear and overheating, and is available with various additive packages and viscosities for different applications. Just remember to adhere to a more stringent oil change schedule -- every 5,000 miles is a good rule of thumb.
High Mileage Oil: Vehicles are lasting longer, and more than 2/3 of the cars on the road have more than 75,000 miles on them. High mileage oil is formulated with conditioners that can swell gaskets and seals to stop leaks around valve covers and other areas where gaskets may have shrunk or cracked. High mileage oil is designed for better viscosity properties, helping to quiet noisy valve-train parts, reduce upper-end engine wear and provide better protection at piston/cylinder clearances which may be a bit looser due to age and wear.
Synthetic Blend: Like the name suggests, synthetic blend oils split the difference between conventional and synthetic, both in protection and price point. Synthetic blend oils are popular for trucks and SUVs, especially when drivers subject them to towing or hauling heavy loads.
Full Synthetic: The jury is in, and synthetic oil outperforms conventional oil in just about every respect. Synthetic is purer and more stable and uniform at the molecular level, meaning better viscosity properties (as mentioned above). Synthetics are factory-recommended for about every new vehicle; they protect against deposits better, are kinder to seals and gaskets and are less prone to vaporize and evaporate. The down side is synthetics are considerably more expensive by the quart, but that's offset somewhat by their 10-12,000 mile oil change interval.
Still in doubt? Be sure to check your owner's manual for manufacturer's recommendations.