Well, obviously a great deal would depend on how the contact was made.
Landing - We come in peace
A landing in an area chosen for its conformation value (in front of the UN/White House/Similar) would obviously have a VERY dramatic effect. Humanity would most likely split into two groups - one looking to the aliens to solve all our problems, the other fearing them as "agents of the devil" or "invaders". Politicians would probably try to appease both groups (at least in a Western country, and many Eastern ones).
Most likely, we'd eventually annoy the aliens enough to make them leave, and then debate why they left for centuries.
Landing - Mars Attacks Style
Hollywood to the contrary, we'd most likely NOT be able to hold off an invasion. Given that they'd need sufficient technology to cross an intersteller distance (Earth, if put together as one, would have just below the bare minimum at present), we probably would not be able to fight back, except possibly with nuclear warheads. If we did THAT, most likely we'd pretty much destroy Earth, and it wouldn't matter anymore who won.
We've been here the whole time, watching.
This would be fairly scary, and would probably result in much the same sort of thing as a peaceful landing, although suspicion would be more in the majority.
We've been here the whole time, running things.
This would be almost as frightening as the invasion option. Pretty much, there would most likely be rioting and civil unrest, but it would probably be put down by human military forces under the control of the aliens. After that, hellooo 1984.
Radio
There would be a great deal of interest for awhile, and a great deal of spiritual debate and such, but then people would realize all we could get from this is conformation they exist, and loose a lot of interest. The only major long-term change would be increased expendetures on space exploration, and a serious study of how to stop an alien invasion.
Unless, of course, such broadcasts origionated from a ship in our system, in which case we would try to talk to them, and the hystaria from possibility one would continue for quite some time.
Um, could we borrow some uranium?
If an alien spaceship crashed, it would most likely be taken to a secret government lab for analysis, and we would try our best to imprison (in really damn secret military instalations) any survivors, and dissect and analize any reasonably intact dead aliens.
Other
I'm sure there's SOME method of contact I've left out, but I can't think of it.
Overall Impact
According to most biologists who speculate on this sort of thing, how well we recieve the aliens will depend on how similar to us they look. We'd obviously be MUCH nicer to cute anime chick type aliens than the hideous insectlike type Ripley and Ash fight. Also, they'd obviously be asked about their society. If it is similar to a type that Earth has experienced, how much a given person likes the aliens might well be porportional to how much they like that form of society. If it ISN'T like anything on Earth (eg hive mind), we might feel threatened or frightened, and give them the cold shoulder (or worse).
I'd write more, but I gotta do homework now. Nice to see you posting, Sarg.
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Seen on a Claymore anitpersonell mine: "Do not eat"
(This message has been edited by Fleet Admiral Darkk (edited 12-05-2001).)