Free magazines are called "Controlled Subscription", by giving the publication your demographics (e.g. income, job title etc), and requesting for a free copy, the publication can sell advertising space to potential advertisers, since they can claim they have X people which fits the profile. The cost of your free subscription is offset by the increased advertising revenue. These demographics are audited by publication audit bureaus. There are many magazines which rely solely on advertising income and the subscription is completely free.
Those 3-5 issue subscriptions are called "Forced Free Trial and Conversion", basically, they send the magazine to you and will bill you at some point, hoping that you will pay and continue the subscription. If you receive these invoices, simply cross them out and write "CANCEL SUB - DID NOT REQUEST" on it, and send it back.
Publishers are required to refund all remaining amounts in the account... i.e. you can cancel right in the middle of a subscription period and get the remaining money refunded.