If you are reloading just to have cheap ammo to shoot, then following the guidelines of trimming in your manual, as well as all of the advise that has been posted so far should more than answer your question.
If you are reloading to make the most accurate ammo you can, then I'll expand on a few things.
Trimming new brass is important for a couple of reasons, including ensuring that your case mouth is square. As the bullet leaves the case, any uneven contact with the case mouth can cause the bullet to pitch in the throat, which will throw off your rifling.
As someone else already mentioned, some chambers are reamed long in terms of case length. For my .300 WSM, for example, SAAMI specs are 2.1" for max case length. Measured with a Sinclair Max Case Length Tool, I find that I can fit brass measuring 2.127 before I will run into chambering problems.
In theory my brass will wear out for other reasons long before I need to trim.
I still trim anyways, every couple of firings. Individual peices of brass will stretch at different rates, even if from the same lot. If you follow your reloading manual, some brass may be at the trim to length while others have stretched to the maximum length. This would give you a variance of up to 0.01" within your lot. Using the Max length of my gun, that could increase to 0.037". That will certainly cause accuracy problems.
Uniform brass is a key ingredient to accuracy, so how accurate do you want to be?
You & me both. Shooting and reloading for my Marlin 1895GS or either of the two Pedersoli's in 45-70, and even when using a heavy crimp, the need to trim has been minimal at best. The same holds true for any other straight wall cases like the 444 as well as a number of handgun cartridges.
