Most styles, especially bigger beers, will benefit from additional conditioning/aging. There are some styles (hefes for example) that are best drunk young & fresh, but they are the exception. Smaller beers generally will improve for 4-6 weeks (or more), plateau for a while, and then slowly degrade. Hop aroma and flavor is one thing that can drop off over longer periods. Oxidation can be an increasing problem if your handling/bottling is not done well. Infections that are minimal or undetectable at the start can become increasingly noticeable with time, etc.
On the other hand, if you brew a bigger, higher-gravity beer; try setting aside some bottles and taste them periodically over months or years. If you have the patience, you'll be rewarded. Aging beers can bring out some incredible flavor changes. If you go to a good beer bar, ask if they have any vintage beers. Sometimes they're more expensive, but other times not so much & then it's a great value & tasting adventure.