As a beginner, I have great difficulty recognizing which dance to do to which music . I would appreciate any advice.

As you progress that will come; trust me.

"Dancing is a contact sport; football is a hitting sport" - Vince Lombardi

This is something which a lot of dancers have problems with, and for most dancers, if they work at it, becomes natural after a while (may be a year or more though)
Dronak is absolutely correct in what he says. And a musical background is a considerable help of course.
It's also important to be able to pick beat 1 of the bar, and this takes a bit of extra skill.
i'll stick to some simple things which might help you - restricting my discussion to Waltzes, foxtrots and quicksteps - if you can pick these reliably, you're well on the way.
1)Play a simple slow waltz that you are VERY familiar with and pick out beat 1 of each bar, counting the beats 1-2-3 with the music. You would be amazed how often dancers get even this wrong in a competition when they are under pressure. How do you recognise beat 1?? It usually has a stronger emphasis. In simple old-fashioned waltzes that you learn on the piano, the left hand has a deep bass note on beat 1 and two chords not so deep for beats 2 and 3. Most social and simple waltzes are like this. listen for it. Viennese waltz is very similar, though twice as fast
2)Do the same thing with a foxtrot which of course is 4 beats per bar. This isn't quite so easy because a lot of foxtrot music has beats 1 and 3 emphasized, though beat 1 is still the strongest.
Try to find the tune "change partners" played as a fox-trot. this starts with the word "Must" on beat 1 and goes like this:
"Must you dance" -3-4 "Every dance" 3-4-
the "must you dance" bit occupies beats 1 and 2.
Try to count it like this and keep the count going as the music progresses. If you feel brave!!! deliberately count it with beat 3 on the word "Must" and you will feel that it's not correct.
3)quicksteps are faster, but still 4 beats per bar, usually with beats 1 and 3 equally emphasized. Only the speed of the music differentiates foxtrot from quickstep (Foxtrot 2 beats per second, quickstep is nearly 4 beats per second)You can of course dance a quickstep slowly to foxtrot music - in europe this is called "Rhythm dancing"
I've gone on too long - hope this isn't too complicated to follow!!
Don't worry - It is frustrating, but it's a skill which is good for your brain and it will come with time.

This a common problem for the beginner dancers, but it usually disappear as you dance.
Advices can be:
When you can't understand current music, just ask your dancing teacher to show you. Usually is very helpfull when someone can count up you the rhytm of the music.
And as second advice: try listening to some teaching melodys, where there is a rhytm only. This practice will help you recognise this rhytms in melody. Many dance music CD's have such teaching trucks in the beginning.

One thing, I do is try the different dances I know to the music and find what I think best fits the music.

I've had some DJ's play what they called a cha-cha, and you watch all the dancers look like they are running, because it's so fast. Hey, I'll do a rumba. And there are some songs that are declared Swing, that I'd rather Foxtrot to and vice-versa. And as long, as there is room. I'll dance what I want. And then you get songs that could be a Hustle, West Coast Swing, or a Cha-Cha.

But one of things that will help you figure out which dance to do is you've got to find the instrument in the song that has the dance rhythm and listen to it and figure out what your body might be doing to follow the rhythm. For example, Waltzes - are typically the piano, and my head does a big drop, followed by 2 beats going back up, and then a drop back down. Tango - a march-like drum, and my head does this whipping back and forth type motion. Salsa - a wood block or cow bell. Swing - drums again, but softer.

Hope this helps...
-TheDitz

I definitely agree with everybody,

Firstly, analyse the ryhtmic properties of dances. This must be your theoretical knowledge about dances and it must be on a strong base. Then, for a while, just try to count the beats and try to find the strongest beat of the music. All dances have a specific beat that is stronger and more meaningful in comparison to the others, so it would definitely help you.

Of course, it will be automatized in time as you dance and dance...

It will come with practice. I'm not sure I could give you a whole lot of specific hints though. I've been playing music practically my whole life, so learning to recognize dances to go with the music wasn't all that difficult for me.

The first thing you should learn to determine is the time signature -- does the music have 3 beats per bar/measure or 4? It could have 2, but for dancing there's usually not a huge difference between 2 and 4. Other numbers are possible but chances are you won't hear them very often. Typically the beginning of every measure will have a stronger (often, but not necessarily, louder) beat and that's your cue that you're on beat 1 of a new measure. If the music is in 3 and kind of slow, the dance is waltz; if it's in 3 and kind of fast, the dance is Viennese waltz. These are the two easiest ones to pick out once you recognize time signatures because they're the only two dances in 3 and the tempo (speed) tells them apart.

Almost everything else is in 4 and it becomes harder to describe how to tell them apart. You should be able to tell a cha cha by the distinct "cha cha cha" part of the rhythm. It should be easy to pick out for most cha chas you'll hear. Tango and samba have characteristic rhythms, but I'm not sure I can describe them well. After hearing them for a while you should start to recognize them. Music for swing has a certain feel that you'll recognize after a while, too. Musically, it's played with what's called "swing eighths" which doesn't really help, but neither does saying swing music has a swing feel, but it does. Swing tempo varies, sometimes the specific version of swing varies with it. If it's fast, but feels more smooth than bouncy like swing does, it's probably quickstep. But there are a number of songs that are fine for both quickstep and swing. Foxtrot will have a sort of strolling, walking feel to it, medium tempo. Rumba is on the slow side and will usually have a latin sound/feel. Not sure I can explain these last two much better.

When you're at socials and can't recognize the dance for the music, ask someone and sometimes also ask how they can tell. Different people may tell you different things and that usually helps. As I started off saying, it will come with practice. The more you hear ballroom dance music, the more familiar you become with it and that makes it easier to tell what dance goes with each song. Almost everyone has gone through the exact same thing. Just keep trying, you'll get it sooner or later. Good luck.

--
James Marshall
marshall@astro.umd.edu
http://www.astro.umd.edu/~marshall