Yes, you can reuse beer bottles. Most people will not use twist-offs, as I believe they are more prone to breakage and/or failure to seal properly. But you can definitely use most of the non-twist-offs found on Sam Adams, Corona, imports, etc.
First of all, the best way to keep your bottles clean is to rinse them 3 or
4 times immediately after emptying. This prevents disgusting mold from building up. Then prior to filling them, just rinse them a couple of times again. To sterilize, fill up a bucket or your sink with warm water and either bleach or a no-rinse chemical such as iodophor, and soak for a few minutes, or overnight if you like. Then rinse if necessary and you'll be all set. A bottle brush is handy to have for the occasional yeast/mold/scum, but as I mentioned, if you rinse every bottle when you're finished drinking it, you will very rarely have any trouble cleaning and sterilizing them.