Previously, you could share your subscription with up to three others, but a rule change quietly went into effect on July 31st, stating this limit had been decreased to one other household member.
Moreover, this person now needs to use the original Prime owner’s credit card to gain access to the benefits. The change appears to apply to new people using the feature; if you’ve been sharing your benefits for a while, you should be unaffected.
For reference, household members get access to Prime’s shipping discounts, Prime Instant Video, Kindle’s Lending Library, Prime Early Access, and exclusive Prime deals. To set someone as a household member, you can check out Amazon’s tutorial here.