For both newer and older engines in good condition requiring a 30-weight oil, I recommend the use of a 0W-30 or 5W-30 CI-4/SL or CJ-4/SM HDEOs in place of SAE 30 and 10W-30. However, 5W-30 and 10W-30 HDEOs would still work well in older vehicles requiring a 30-grade oil. Oil burners (ie, gasoline engines that consume a lot of engine oil) should stick with 10W-30 HDEOs for its lower operating cost. The only 0W-30 HDEOs I've been able to locate so far are listed in the Heavy Duty Engine Oils article. Because 0W-30 has a lower viscosity than 10W-40 or 20W-50-oils that many people like to use, a 0W-30 oil will have less internal friction and will have better heat transfer through the engine thereby carrying away more heat to the oil pan and filter for cooling. In other words, lower viscosity oils tend to run cooler. Because the 0W-30s are synthetic (or semi-synthetic) oils, they also have extremely low pour points that even suitable for arctic winter operation and there would be no need to change to a lower viscosity oil for cold weather use.
Dual API ratings (like CJ-4/SM) means that these oils are suitable for both gasoline and diesel engines at the expense of potential slight fuel economy savings (due to the lack of friction modifier additives). CJ-4/SM oils are safe for use in modern vehicles equipped with catalytic converters requiring 10W-30 or 5W-30. You may also safely use this in air-cooled engines requiring SAE 30 engine oil. Engines requiring a heavier weight oil such as 15W-40 may safely use a 0W-40 oil for improved fuel economy and reduced start-up wear. Engines with aftermarket high rate valve springs and high lift camshafts will benefit from the higher ZDDP levels in CI-4 oils but these are getting harder to find. However, CJ-4 oils generally have backwards compatibility with CI-4+, CI-4, and CH-4 oils. However, engines from the 1960s and 1970s only required API SC to SE so modern oils would still offer more protection than originally specified by the OEM.
Synthetic 0W-30 HDEOs are more expensive than conventional oils. If price is an issue or if 0W-30 oils are not readily available in your location, many engine oil manufacturers also make 10W-30 HDEOs which should work similarly well as 0W-30 oils in gasoline-powered vehicles in warm weather. For summer-time use, older vehicles often were recommended to use 20W-40. In this case, a 15W-40 would be an excellent (and very economical) substitute. Very thick oils like 20W-50 are generally not required in street-driven engines and will waste both power and fuel economy under normal operating conditions. Many BITOG members prefer using high-mileage oils (such as Quaker State Defy - with API SL for 10W-30) which tend to have higher levels of ZDDP than Starburst oils.