Anything landscaping-wise I can do with a poured concrete basketball court?

You could just use it as a patio. Do some landscaping around it, add a couple of tables, chairs or other seating areas, maybe one of those chimeneas or free standing firepits. A good quality swing in a cradle. Or you could paint squares onto it and turn it into a giant chessboard. Here is an online source for the pieces: http://www.target.com/s?keywords=giant+chess+set&searchNodeID=1038604&ref=sr_bx_1_1 You could also do checkers with round pillows instead. Maybe a pergola or sunroom or arbor? How about setting up a hot tub or spa on it? I think you could use it for the greenhouse too. You could get one of those pre-fab kind and just set it on the concrete.

You can put a greenhouse on an existing slab.

I can't see why a greenhouse couldn't go there. You can drill into the concrete to fasten things to it. Or tile it with something interesting that isn't slippery when wet, install some large planters and a gazebo and one of those outdoor kitchens, maybe put a fence around part of it, and call it a patio or terrace or outdoor entertainment area. I kind of envy you, actually. You have a nice flat space that you don't have to mow. I could use one of those from time to time.

It's a patio. Some people pour concrete for patios. They probably had a table, chairs, grill, lounge chairs, and etc. out there. You can now buy or have installed a roof over your patio. They are very pretty and a protection from all kinds of weather. Look in your telephone book for patio builders.

Make it a party pad. Put a grill some chairs and tables on it, then let the good times roll.

Do you want a structure there, or are you more interested in using this as a living space in the yard? A half basketball court would be a really big home greenhouse -- expensive to heat! If you wanted a structure on the site, you could do a combination of things -- maybe a workshop with a lean-to greenhouse on the south side with perhaps a child's playhouse and a bit of patio incorporated into the plan. You do not say how substantial a slab we are dealing with here. Is it deep enough to be used as a footer for a building? If so, the aforementioned TapCon-type screws into the existing cement should work. If not (likely), then you could build good footers around the edges if you wanted a building that big or jackhammer out the necessary part if you want only part under cover. If you like to work on cars, even a minimalist structure to keep out the rain will make that basketball court into a place you can really use. If you choose not to build a structure, then we are talking about how to make an ugly rectangle beautiful and useful. I'm gathering that the plainness and shape leave you cold. How about doing some stamped-concrete add-ons in colors to make what is there look more beautiful? You could cover that ugly concrete with beautiful pavers or slate and tie it to the architecture of the house. The pergola idea with perhaps a chiminea sounds lovely. You could surround your outdoor living room with plants that smell lovely like roses, ceretain high-fragrance daylillies, and of course nicotiana (an annual flower that blooms at night) for night scent. If you like the Williamsburg idea, plant boxwoods nearby with their spicy scent. Need to screen out the neighbors? Your local garden center stocks lots of bushes that provide winter interest, stunning fall foliage, and even stunning flowers during part of the year. Are you a do-it-yourselfer? A paved area in the garden is a blessing.

I think the center of the backyard will look fabulous with this kind of Gazebo- can you just imagine how nice it would be having this screened Gazebo to put wicker furniture in, or a hammock on its own frame, without having to worry about getting eaten alive by mosquitos on summer evenings! http://www.google.com/products/catalog?q=steel+gazebo&rls=com.microsoft:*&oe=UTF-8&startIndex=&startPage=1&rlz=1I7ADSA_en&um=1&ie=UTF-8&cid=15292100884177783424&ei=CfQGTb6oB8G88gbo4r3BCQ&sa=X&oi=product_catalog_result&ct=result&resnum=2&ved=0CCUQ8wIwAQ#

Clean the pad build or buy already made arbors.Grow some vines throw some chairs WA-LA you have simple inexpensive shaded sittin area.

My top five ideas. Build raised garden beds on it and grow stuff in no-dig gardens. Bust up the concrete and use the pieces as landscaping rocks. Get a tennis net and make it a tennis court. Lay some natural fibre carpet on it, then plant lawn seed on the carpet. Over many years, this will build up into a good layer of soil, and will remain level. Get lots and lots and lots of plants in various sized pots and arrange them artistically all over the slab. Pay big money to have it ripped out and rehabilitate the soil underneath...then do any of the things mentioned above. Pur ramps and stuff on it and make it a skate park.