This greatly varies and depends on the type of motor (NA, Boosted, Daily Driver, DD/Street Strip, etc). To start, to read oil properly the first number will be a winter/cold weight (has the W after the number, such as 0w-30, the 0 is the winter weight viscosity)...where the second larger number is the normal operating/hot viscosity.In colder/freezing climates the winter weight is much more important then in hotter climates. When oil is exposed to very cold temperatures, as all liquids it causes a reaction in which the oil thickens. If it gets too thick, it will not pass through the motor sufficiently, thus starving your motor and bearings of oil, causing damage. If you are in a freezing climate, it's best to stick with a 0w winter weight. Now the normal operating/hot velocity number is for normal operating temps. At this point you will want to refer to the below writing.
------NATURALLY ASPIRATED/DAILY DRIVER/NITROUS MOTORS ------------
In normal, low mileage motors (less then 100k miles) it's best to stick with the oil weight Honda recommends (0W or 5w-20). In hotter climates, we have found it's best to run a 0/5w-30 oil, as oil tends to thin out or the velocity lowers as the oil is heated to higher temps. This also hold true for motors OVER 100k miles, as the thicker oil and viscosity can fill in the worn bearing and also tends to not leak from seals and gaskets, as the thinner oil would. All motors break in and wear over time, which is why we suggest the 30 weight oil on motors 100k miles +. IN ALL CASES, THE BEST OIL TO RUN IS FULL SYNTHETIC. IF YOU ARE RUNNING CONVENTIONAL OIL, YES, YOU CAN SWITCH OVER TO FULL SYNTHETIC BUT MAKE SURE YOU KEEP USING IT, DON'T SWITCH BACK AND FORTH FROM CONVENTIONAL AND FULL SYNTHETIC. It should also be stressed there is a HUGE difference between Full synthetic and Synthetic "Blend". A synthetic blend is exactly that, it's a blend of conventional and full synthetic.
-------BOOSTED/HIGH HP (500WHP ++) MOTORS-------
In a sense a boosted motor is causing hell to the oil, heats it up and cause multiple potential issues if the correct weight is not run.
Oil is the life blood of any motor, but even more so in high HP or Boosted motors.The oil pass through the Turbo to lubricate and help cool the turbo, in doing so heat is transferred into the oil from the very hot turbo. This will once again thin the oil (lower viscosity)and could cause the oil to actually overheat, become too thin or even start to burn off. In many cases you will want at a bare minimum 30 weight oil, or what we run in our 600hp daily driven J32a3 is 40 weight oil (FULL SYNTHETIC). If your motor is on the older side, this again will help fill in the large bearing space, but also exposed to high heat the thicker oil can actually fill the space in, where a thinner oil could not. Also, many race engine builders add in extra clearance to the bearings to allow more oil to be between the bearing and the journals, as the crank/rod journals do not ride on eachother, they literally ride on a cushion of oil. In adding that extra clearance, it also provides the crank/rods extra cushion to be held at higher loads, too thin of an oil and it will simply be pushed right out of the bearings oil pocket/clearance.