Yeah hoppy beers you want to drink fresh. The flavor of the hops fades over time so it won't taste as good later on. It won't be bad for you like spoiled milk or anything like that, just won't taste the way it's meant to. Big beers like imperial stouts, quads, and barleywines can be aged as the hops aren't really the focal point in those beers and the harshness of the high alcohol content will mellow out.
There is some disagreement on certain varieties though, for example many say if it's a coffee stout it should be had fresh before the coffee fades out. Bourbon barrel-aged stouts some say are better fresh before the bourbon flavor fades, but the rest of the beer sometimes will improve if you let it age for a while, so it's up to you to do some experimenting and see what aspects of these beers you want magnified when you drink it. Sometimes for bourbon barrel-aged stouts I let them sit a few months so it mellows out without the bourbon flavor disappearing.
I like to age beers and then when I'm going to drink it I buy a fresh one so I can do a comparison. When you do this with the same beer of a few consecutive years, it's called a vertical. It's interesting to see how the beer changes from year to year.
If you're going to age beer, ideal conditions are a cool, dark place I think around 50 degrees. Keeping beer refrigerated will slow down the aging, so if you're aging beer you don't want it just sitting in the back of the fridge for months. The top shelf of a closet or something is probably a good spot. I keep my aging beers in a kitchen cabinet. It's probably not the perfect conditions since it gets hot in there sometimes, but I don't have a basement so it's good enough for me.