If you're an American curler, you probably get the USCA produced United States Curling News during the season. It's a fine publication (except for Cocky Rocky), though it has more of a newsletter feel to it. If you want to expand your curling world view, it's absolutely necessary that you subscribe to the (Canadian) Curling News. This independent publications has been around for a long time, and they cover curling from Canada and the world. They feature talented writers covering all sorts of relevant topics.
Email info[at]thecurlingnews.com for more information, or just subscribe via the website, and you'll be contacted about your gift subscription.
Don't forget to check out the rest of the Gift Guide and stay tuned for more!