I believe giveaways really help.people like freebies and just like bees to honey,it really a bait to get people.This will help to pull traffic and organic one at that which will help a blog or forum to succeded. Of course we know without traffic a blog is good as dead. 

Yeah. It kind of works. I'd only suggest doing them once you have a large user-base though. If you start doing them with a small user-base, barely anyone will participate. If you promote this giveaway off-site, someone will most likely join for the giveaway and soon leave once it's over.

Do you think it's a good idea for a new forum to use it to encourage people to sign up and post? The idea being that they get hooked?

It works sometime, i did try giveaways in the forum but it didn't pick up as my forum was regional based and i had very few active users.

Contests and giveaways will always work. People like winning things and getting stuff for free. Whether it will work on your site is completely up to you. You need to market your site well and promote your contests and giveaways well. If you do, you'll find an increase in traffic and participants for your contests.

Throwing a giveaway or a contest of some sort in your forum or blog will always boost the activity and lead to more traffic. People like to get rewards for what they are doing. Also, it's a great way to promote your website. For an example, if a person is just starting a new forum and make a contest where the top poster at the end of the week win $20 there will be much more activity than regular. But usually the increased traffic remains still for the period of the event. After that most people just go away because they only wanted to grab the prize. But there is also a chance for some of them to stay just because they like your site or in hope of future giveaways.

Giveaways will definitely benefit your website. People like freebies, just like fishing with a lure, people will take the bait. It's human nature

This will help to achieve pure organic traffic which could increase your search engine rankings. The end result of giveaways is increased visitors, members and traffic which could mean more Ad Revenue if your looking to earn cash. 

The freebies will help but only if you can afford to keep doing it because everything costs at the end of the day and no matter what once you stop them freebies the people who come for freebies will leave.

yep, it does help a lot. Sadly though once things are said and done the traffic vanishes.

From my experience, giveaways generally don't work all that often. It's a good idea but it's not always one that pans out well. People like freebies and if you're doing something like say a Posting Contest, most people will eventually get tired of making genuine posts and start posting one liner responses such as "Ok." "Yes" "I agree"  just to get their post count up to win said giveaway.