Why not cover a plain sturdy table with a nice cloth?

There are a lot of choices in this regard, one big issue will be what you'd like to do with the table when not using it for dining. There are coffee tables that rise and convert into dining tables, small console/side tables that fold out into larger tables (and models that even integrate the chairs), traditional folding tables that fold flat for placing in a closet, tables that connect to the wall and flip down, etc.

If you are going to have to move all the furniture out of the way anyway, then I suspect that getting a double-duty coffee/dining table will work best - here's a nice one: http://www.jensen-lewis.com/product.php?pid=00000316

Other good places to look include the old standby Ikea as well as Laytner's Linens, which is particularly good for more traditional options.

I have the same issue and just recently solved it by purchasing this gate leg table from Surprise Surprise:

http://www.surprisesurprise.com/products/Gate_Leg_Table.328.html

(It looks better in the darker finish.)

When not in use, I store it behind my loveseat and it doubles as a sofa table.

Susan - I had a similar problem and found an excellent table on Craigslist that folds out. It seats 2, and can be expanded with a leaf to seat 4, and then has fold down sides that lift up to seat 8 facing each other (and 10 if you squish some suckers on the end!). It doesnt have a make on it, and its kind of shaker looking so i keep it covered with a tablecloth.

The door store has a number of tables that extend - http://www.doorstorefurniture.com/enterprise.html that arent bad looking (though they dont fold away entirely). We're embracing ours as extra storage and stick things under it when not in use.....

The big problem is knowing where to store any folding table (or plywood overlay, etc).

This may seem a bit odd, but for a time, I used a large table with folding legs as a headboard (all of my underbed, etc storage had been long since taken).

This isn't exactly what I had, but it is close. You could also use something where instead of folding flush, the legs unscrewed.

http://www.target.com/Hostess-Folding-Table/dp/B000R9NTM0/qid=1193855017/ref=br_1_7/602-9462470-4619835?ie=UTF8&node=14053501&frombrowse=1&index=target&field-browse=14053501&rank=pmrank&rh=&page=3

When it wasn't dinner party time, I had a chunky modern looking wooden headboard. When it was time for dinner parties (or taxes, or anything else that required a lot of storage space), I could slide it out and into the living room and have presto entertaining space.

I work in a busy restaurant and here's what we do. When we need extra tables we use plastic folding tables (from Home Depot or Lowes) and cover them with table cloths. They can seat 4 on each side and one on each end...10 total. They fold in half and are very sturdy. Very easy to handle and store....not heavy.

I'm not sure just how tight your space is but this table is working beautifully in our small place. It's a perfect coffee table and then it lifts and opens to seat six.

http://www.dinettica.com/productdetail.asp?modid=519

a creative way:

- buy two of these rad yellow steel sawhorses at Home Depot
http://www.homedepot.com/webapp/wcs/stores/servlet/ProductDisplay?storeId=10051&langId=-1&catalogId=10053&productId=100003259&categoryID=502727
and keep them in a closet or under your bed

- buy a sizeable piece of sturdy plywood which will serve as your table top. have an artist friend paint or draw a mural, painting, graffiti, collage, etc on one side of the plywood. mount the large piece of plywood (now art) as your headboard, above your couch, or propped against a wall (you can have the art done long ways or tallways).

then, when you have a dinner party, you just clear some space, get the sawhorses out of the closet, and use the plywood as the table! you can use the art side up or flip it so that it doesnt get damaged.

i've totally done this and its really fun.

I have two regular square folding tables, but cover them with these awesome corduroy tablecloths from my Grandma's bridge-playing days. That makes all the difference, and the table doesn't need to be decorative at all.

goodnightdean beat me to the suggestion I was going to make, so I'll just add:
1. you can mount 1x1 strips to the underside of the woodboard to prevent slide-around.
2. if you're clever, you can probably add hinges to the board so it can fold in half. maybe.
3. decoupage!!!

Although I really like siobhan's headboard/secret-table idea.

Whatever you consider, carefully analyze leg placement with regard to chair placement. Many "magic" convertible solutions are useless in reality.

Personally, I use a Danish modern teak table with self-storing leaves at either side that nearly double the length. I don't know who made mine, but Crate and Barrel has an uglier version in "espresso" or something of the sort. I supplement it with the unbeautiful but table-clothed http://www.target.com/Banquet-Folding-Table/dp/B000BK3IBC/sr=1-2/qid=1193862519/ref=sr_1_2/602-5907575-1409429?ie=UTF8&index=target&rh=k%3Afolding%20table&page=1

If that link doesn't work, just search "banquet folding table" at http://www.target.com

http://ligne-roset-usa.com/?sec=products&pid=11&cid=17&rid=181&page=3

they have 2 different versions of these coffee tables that convert into dining tables. this one becomes a bigger square, the other, a rectangle. good luck.

When I want tables* for an event, I admit that I find it easier to just rent them. I know, sounds insane for just a dinner party, but there's a rental place around the corner from me and if those guys are out of tables then the other places in town deliver.

Then, on the 364 other days of the year when I don't need so many tables, I just don't have them.

It also means that if I want small tables I can rent small tables, or one large table, depending on what I need. And all those chairs, too. Plus serving dishes, extra plates and glasses, and any linens. Not having to store all that stuff for the occasional party is really nice. Rental rates are pretty reasonable, too.

*I don't live in a tiny apartment, so I already have a large dining room table, but this idea is adaptable.

Thanks for all the advice everyone! So many great options. If anyone has and extra one of those convertible Ligne Roset tables hanging around, let me know. I'll happily take it off your hands.