One way to make a flexible shelf area is to use one of the prefabricated systems available at your local home improvement center. These systems usually involve tracks that are mounted to your walls and modular pieces that lock into the tracks. The modular pieces are customized for various uses, like ones with hooks for hanging clothing.
The upside of these systems is that they are fast and easy to install and easy to change later. Shelves can be moved up and down the track or removed altogether in seconds.
The downside is that they have a very industrial look, which is mostly appropriate for an office or utility room application. They also mount to your walls, so moving them is a bit of an operation. This can be worked around by building a cabinet and installing the track system inside, but if you're going to go to that much trouble, you might as well build the whole thing.
Shelving from Scratch
Another way to make a system with removable shelves is to build it yourself from scratch. In this way, you can make your shelves as attractive or industrial as you like. The most accessible material to build your shelving system from is wood. What type of wood is up to you, depending on the aesthetic you're going for, but plywood is always a great option. Plywood stays flatter than stick lumber and doesn't bow when ripped to width. You can get plywood with hardwood veneers like walnut and maple, and finishing the edges with some edge banding will fool anyone into thinking your shelves are solid hardwood.
For this method, build a freestanding bookshelf that will fit in the space you have. To make your shelves removable, you'll need to give them secure slots or supports to rest on. You can do this by cutting dado slots at regular intervals in the upright supports of your shelf cabinet or by attaching resting blocks. The most important part of making removable shelves secure is making them thick enough that they won't bow under the weight of what's on them. If they bow too much, they could slip out of the slots, and you'll have a mess to clean up. Just remember to make your slots slightly wider and longer than your shelves, to make removing the shelves easier.
The upside of building your own shelves is choosing the finished look. Also, making shelves like this does not require attachment to the wall, so you can move them around the room to redecorate more easily than track systems.
The downside is the time and money required to build them. Hardwood veneered plywood can get expensive, and you have to have the time and tools to build your own shelves.