There isn’t a huge reason to buy online or in the store when you’re buying a product like an Airport Extreme. The prices will be the same on the Apple Online Store and your local Apple Store. Promotions and special offers will also generally always be the same. The biggest difference would be if you want it delivered to your house or if you want to go pick it up immediately.
You can get education and military discounts both online and at the retail store.
If you are buying a computer the benefit of buying online would be that you can customize the computer (change the specs of the hard drive, processor, graphics card, etc). In the stores you can only purchase a stock model and upgrade the RAM. Note that if you customize the computer online you can’t return it after you purchase it, so be aware of that.
On the online store you can also order refurbished computers and iPods and other products, which are usually quite a bit cheaper than a brand new model. They have the same warranty as a brand new one and work just as well. I almost always get my Macs refurbished, personally. Save a few hundred bucks (especially on older models) and they are the same thing.
In the retail stores however they usually have a “Fire Sale” once a month where they sell all of the items that have been returned to the store because the buyer didn’t want them. Sometimes you can find amazing deals on those types of things. Ask an employee when they do their fire sales and see when the next one is.