We have a service where we literally give away free money.
Naturally said service is ripe for abuse. To defend against this we do the following:
log
First, I suppose (hope) that you don't literally give away free money but rather give it to use your service or something like that.
That matters as there is a big difference between users trying to just get free money from you they can spend on buying expensive cars vs only spending on your service which would be much more limited.
Obviously many more user will try to fool the system in the former than in the latter case.
Why it matters? Because it is all about the balance between your control vs your user annoyance. I see many answers concentrating on the control part, so let's go through annoyance, shall we?
Log IP address. What if I am the next guy on the computer in say internet shop and the guy before me already used that IP? The other guy left your hot page that I now see but I am screwed because the IP is blocked. Yes, I can go to another computer but it is annoyance and I may have other things to do.
Collecting physical Adresses. For what??? Are you going to visit me? Or start sending me spam letters? Let me guess, more often than not you get addresses with misprints at best and fake ones at worst. In fact, it is much less hassle for me to give you fake address and not dealing with whatever possible spam letters I'll have to recycle in environment-friendly way. :)
Collecting phone numbers. Again, why shall I trust your site? This is the real story. I gave my phone nr to obscure site, then later I started receiving occasional messages full of nonsense like "hit the fly". That I simply deleted. Only later and by accident to discover that I was actually charged 2 euros to receive each of those messages!!! Do I want to get those hassles? Obviously not! So no, buddy, sorry to disappoint but I will not give your site my phone number unless your company is called Facebook or Google. :)
Use signup captcha. I love that :). So what are we trying to achieve here? Will the user who is determined to abuse your service, have problems to type in a couple of captchas? I doubt it. But what about the "good user"? Are you aware how annoying captchas are for many users??? What about users with impaired vision? But even without it, most captchas are so bad that they make you feel like you have impaired vision! The best advice I can give - if you care about user experience, avoid captchas as plague! If you have any doubts, do your online research first!
See here more discussion about control vs annoyance and here some more thoughts about being user-friendly.