I laughed at the HGTV idea because just yesterday we were at my mom's house and she was watching one of those "get your house organized to sell" type of shows. I commented that we need a "get organized to homeschool without going crazy" show. Maybe we should start an e-mail campaign?
One thing I've liked using are tower bookcases with baskets for each shelf. This keeps things organized yet not visible. I like that because visual clutter makes me tense. Plus, I love baskets! I also have three large Peterboro magazine baskets. http://www.peterborobasket.com/
These were a gift from my sister and I just love them. They can hold many of your supplies, such as pencil boxes and other small totes. You could easily keep your teacher's manual and all the books you are currently working from in one of these. It is easy to tuck in a small cd player with some audio books and/or your current read alouds. They are portable, of course, so you can tote it to wherever you plan on sitting to read or teach. When I want to keep these on the floor and not have the items being stored inside visible, I simply take a section of fabric that matches our curtains and neatly lay it across the basket and raise the handles. Very pretty!
Another little trick I used one year was to buy the small, individual sized whiteboards at Wal-Mart and use the adhesive tabs which come with them to stick them onto the back of each child's 3 ring binder. Presto, instant portable whiteboard for working math problems, practicing spelling, or playing games like hangman. For a while, this can easily take the place of a larger whiteboard or chalkboard. You actually could also hide a whiteboard behind a pretty curtain - I have one which is hung under a smaller, high window - cover with a valance and when not in use it actually looks like it is just part of a larger window.
Specifically for HOD, you can do some clever things. For instance, my son is creating a stair-step timeline. This could be done on a presentation board which can be folded and tucked away when not in use. You can also create a timeline on poster boards (adhered together on the back with tape) and at least be able to tuck it into a closet or under-the-bed storage area when not in use.
I do know some mom's who use under-the-bed storage boxes to keep their HOD books which are not currently in use. This way, the kids can't dive in and read them all ahead of time, and they are clean, dust free and out of sight. I don't do this because I like to be able to vacuum under the beds without moving stuff around.
Oh, another favorite trick I picked up from a homeschooling mom of 7 was the wooden file cabinets. She had two wooden file cabinets in her family room. They were the 2-drawer type oak type. She had them at each end of their sofa, with the drawers opening to the back. Walking into the room and sitting down, you really didn't notice these were file cabinets. She could just walk around behind the sofa to access her file drawers and her bookcases as well. (Obviously, this only works if a) your sofa or chairs aren't up against a wall and b) you feel you need to hide the drawers!) Two of those file cabinets can hold an awful lot of books in hanging files, or small flip-top totes for art supplies or what have you.
Evaluate your existing space. Is there a linen closet you can live without? Kitchen cabinets that could be organized more efficiently, thus freeing up some space for homeschool storage? What about investing in something on wheels that can be set aside at the end of the school day - a small, oak kitchen island works well. I have this one and I love the portability of it. http://www.walmart.com/catalog/product.do?product_id=10072814
Some have even purchased a library rolling cart - this can hold all the books and supplies and then be rolled into a closet at the end of the day. (They are expensive, though!)
Lastly, don't neglect to consider some trunks and/or a hope chest. I have three antique wooden tool chests (one is the size of a small hope chest, the others are smaller), plus my own hope chest. I keep these in our piano room mostly for decoration, but they can be easily used for homeschool storage.
I hope some of these ideas help. I'm not the kind of mom who resents homeschool clutter - this is my full-time job and I love it and am proud of it. So, I'm more the type who wants our timeline visible and proof of our work in a prominent location. . .just as my friends with public school kids have tests plastered all over their fridge!
Yet, I've used these ideas throughout the past 9 years to keep things under control because we have a small house with no storage (ie, only 3 closets and no attic or basement. Eek!)