Best Family Plan
If you're looking to save money on your monthly mobile bill, then signing up multiple lines is the best way to go. The Big Four carriers (AT&T, Sprint, T-Mobile, Verizon) don't really have "family plans" anymore, per se, but they do have multi-line plans that are similar to buying in bulk. The more you add, the more you save.
Here's the best family plan you can get from the Big Four.

Best family plan: T-Mobile

T-Mobile
Since all the major carriers switched to unlimited plans, T-Mobile has taken the lead in terms of savings with a family plan.
You can sign up to four lines on one account for $160 per month ($40/month/line), taxes and fees included. With each line, you get "unlimited" data (up to 30GB of 4G LTE, 2G speeds after that), unlimited talk and text, Music Unlimited (unlimited streaming from select services with no data charges), and tethering at 3G speeds.
With certain services, like HBO Now, you can also stream as much video as you please without extra charges, though video streaming quality is throttled to 480p. If you like your HD video, you'll have to compromise.
Though T-Mobile's coverage still isn't the best in the country, it's quickly catching up to Verizon's wide reach.

Runner up: Sprint

Sprint
Sprint may not play nice when it comes to bringing your own device, and its CDMA technology might be a little dated, but Sprint's "Unlimited Freedom" plan costs just as much as T-Mobile's for four lines, and you get HD video streaming and 10GB of hotspot data per line. You'll also get unlimited talk and text and 2G data.
The first line is $60/month, the second is $40/month, and each additional line is $30/month, so four lines are $160/month. This does not include taxes or other fees.
If you prefer Sprint's service, or you're already with Sprint and are considering resigning, know that you'll get roughly the same deal as T-Mobile.

For your consideration: Verizon

Verizon
Verizon may not have the best deal on family plans, but it does have the best coverage in the U.S., and its multi-line pricing is still competitive.
Verizon only offers multi-line plans on its unlimited data plans. Four lines are $180/month (taxes and fees not included). You get "unlimited" data (22GB of 4G LTE, possible throttling to 2G speeds after), unlimited talk and text, HD video streaming, tethering, and service in Mexico and Canada.
Like Sprint, bringing your own phone to Verizon is a bit difficult, but if you want the best coverage available, then check it out.

The other guy: AT&T

AT&T
AT&T may be the second biggest carrier in the U.S., but its current unlimited family plans are a bit difficult to parse. For its "Unlimited Choice" plan, AT&T's site says you can get 4 lines for "less than $40 per line, per month", but the exact price isn't listed anywhere. You'd have to speak directly with an AT&T rep to see. You can, however, have up to 10 lines on one account.