Years ago my church switched from mailing church items (newsletters, flyers, forms, and more) to putting mail in a mailbox at the church with the idea that each home could pick up their mail each Sunday. This took a lot less time for church staff since they didn't have to stuff envelopes and address labels, and they didn't have to pay postage. From what I have seen a lot of other churches made similar transitions for the same reasons.
In the last several years a similar transition happened with churches forgoing printing many items and then mailing or placing them in mailboxes. Actually, this has happened with almost everything from credit card bills, to birthday cards from friends. Similarly, this is much more cost effective (no postage, printing, or supplies) and is much quicker, allowing time-sensitive items to go out immediately.
So, you probably didn't even need convincing that disseminating information by email is faster, cheaper and easier. While you may be inclined to just email your whole church there are several services that make it easier, and more friendly (for both you and the receiver). Services like Mail Chimp and Constant Contact make it much easier to manage your subscriber lists, easier for users to unsubscribe, and keep your messages not marked as spam. They allow you to see what messages get delivered, see how many people actually read or look at the message, and help with formatting and creating templates for your messages. Just keep in mind that there's probably a few people that you should continue to give hard copies to.
While both services cost based on the number of emails sent per month and the number of subscriber, Mail Chimp has a plan that is free, while Constant Contact has no free plans. Mail Chimp is also just a little bit better in several ways.
So, if your church has considered emailing more items, consider using one of these services (especially since Mail Chimp is free), that in the least will help you avoid dealing with postage, stapling newsletters and printing out hundreds of copies with the occasional printer jam.
How does your church send out emails?