How effective it is to give away prizes to increase subscriptions in a blog?

For example offering a gift card, t-shirt, etc... to people who sign up to your blog or website in general... does this work? is it worth it?

It can be very effective. While I have never ran one of these contests myself, I have participated in a lot of them, and I have seen a lot of them succeed.

The problem you will have (which is your current problem) is getting the word out. You need to get other bloggers to spread the word for you. Do this by making one of the ways to enter the contest be posting on their blog. Also, reach out to other bloggers in your niche and tell them about the contest.

The problem with prizes and sweepstakes is the legal disclaimers and rules required for them. Make sure you spend time doing research on sweepstakes rules for your county, state and country. In the USA it is very strict to ensure that family members, employees or principals dont rig the sweepstakes. Sometimes, in the event of a raffel or lottery the winnings must go to a non-profit or charity.

Can be good publicity. In the USA you could never charge for participation in a program.

The two problems are:

1) Legal. Depending on your audience you may have to worry about multi-region/country legal differences.

2) Who you attract. You want to attract people who will use your site and stay and make you money. If you site is all about, for the sake of an example, selling fairtraded CO2 neutral bags, and you have a competition that gives away a free Hummer - you might get a lot of entries, but not a lot of them will be interested in your site.

The second point is the big downside of competitions in my experience. I've seen a lot of people run successful competitions that get lots of entries. In most cases those entries to not turn into a large number of repeat customers.