tulip table authentic or fake?  

Burke
From what little I know, I'd suggest studying images of the real Knoll products and then looking at old repros from Burke.
Many times I've thought I'd found a Knoll table when in reality it was a Burke knock off.

I have owned
a Burke table before. The top of the base was square and affixed to the table top with screws. The real Saarinen bases are round at the top and affix seamlessly up into the bottom of the table top creating a continuous, smooth curved line.

Here's my two real geniune Saarinen Tulip pieces
both are made by Knoll and both are vintage, judging by the condition!
(Thanx for fixing the sizing)

I know it sounds rudimentary...
but I always check for a sticker on the bottom that says "Knoll". The majority of tables and chairs that I have come across have still had the knoll sticker affixed to them. I can't remember if they had the patents listed (as does the Eames lounge chair)or not. But if they do, look em up on freepatentsonline.com. This is a great site to do research into design of anything. And it will tell you who the designers were, as well as the parent company.
An easier alternative to this is to check eBay and look up "tulip chairs", "tulip tables", "Knoll tulip", "Knoll Saarinen Tulip Chair", etc. Look up "Burke tulip" too and save the HTML files and images into a folder on your computer for comparisons. eBay is the easiest way, in my opinion, to gain experience in telling fakes from the originals.
On eBay: Note that if it says "Knoll style" or "Saarinen style" its a dead giveaway that its a replica. Also, originals usually sell for much more than copies (for example: If its a brand new tulip chair selling for $199 as opposed to the original which sells for $999 new, you can be pretty certain its a copy). The thing with copies is that they can be pretty close. However, to avoid copyright infringement, they will always be "off" in some way. Or they will add extras not incorporated in the original design (for instance, some Eames chair copies have metal bars to reinforce the back; something unknown to the original). And if someone says "I'm not sure if its an original or not" he's probably trying to sell you a copy.
Anyway, hope this helps. All the best!
Chris C.

I inherited a Burke copy,...
I inherited a Burke copy, looks fantastic. Virtually indistinguishable from the originals by sight. Give away is the underside which has 4 screws holding the top to base and darker walnut wood. Very happy with mine!

Base
Is made by Alcoa.

I went to the
"Shaping The Future" exhibition that's running here in Minneapolis at the Walker Art Center. It's apparently a "major" exhibition (it's split between the Walker and the Minneapolis Instutute of Arts), but the Walker installation (supposidly comprising of the furniture) was something of a disappointment.
There were only a handful of pieces on display:
1 Grasshopper chair without the ottoman in solid blue hopsack fabric and the plywood is the dark (walnut, I think)
1 large marble Tulip conference or dining table that is not real old
1 Tulip side chair in black
1 Tulip armchair in white with the standard red hopsack cushion (looks new 'cause the base is glossy)
1 Organic chair with the wood legs
1 Womb chair and ottoman with the most standard, boring oatmeal fabric
1 high back Organic longue chair with the wood legs
1 leather armchair on a chrome base that I could identify (and there was no informative plate for this chair)
That's it.
No Tulip stool
No Tulip small round or oval side table
No Tulip coffee table
None of the side or armchairs...you know, the upholstered ones or the side chairs with the plastic back
No Womb settee
I realize that Saarinen didn't do alot of furniture, but there should've been more.
I also bought the accompanying book, which only has a 12 page chapter on Saarinen's furniture. There's some smallish photos of some cool prototypes and some nifty more detailed quotes from Florence Knoll about Saarinen's beginnings at Knoll.
So, I saw the exhibition and got the book, but I'm actually a bit disappointed.

Tulip spotting vintage real knoll
The precise curvature of the real tulip is unique and easy to spot. Vintage knock-offs use some variation. Knoll tulips have no visible screws. All the tops screw down onto a single threaded rod on top of the base. When the top is in place you can see no mechanical connectors between the top and the base. To my eye this continuity of the surface, even where you may not often look, is what makes the real Knoll Saarinen Tulips sweet. That and there is a very satisfying ease to the curvature on the real thing.

From what I've understood,...
From what I've understood, unlike the stools & chairs, the small vintage US-made Knoll Tulip side tables were not stamped underneath the base, but had small stickers under the top instead..and of course the stickers sometimes fall off, but I think the legit tables can be recognized pretty easily, at least by a trained eye. Here's a couple pics of two tables (the latter, without a sticker, used to be mine - note the original off-white color underneath the base) which pretty much tell the story (then again, the current Knoll tables most likely look different...):

authentic table and 2 chairs
How much are an authentic Saarinen dining table with 2 original Tulip chairs with arms worth?

I could be wrong...
but on all the REAL Saarinen pieces I have ever seen the two "sides" of the stem were never completely parallel, meaning an elegant curve remained throughout the stem. We have Authentic vintage side chairs and a knock-off table in which the stem is parallel towards the middle. Not sure if that helps but it is something to watch for.

target...
target has a saarinen look-a-like side table called the 'trumpet table'. it's all metal and comes in black and white. for $30-40 it's a great buy.
Jer