I recently received an email invitation for a friend's bridal shower. A few weeks before this, I received an email baby announcement from my cousin. And a few months previous to that, I had two baby showers where the invitations were sent via email.
Although the email wedding announcement that I recently received seemed to be a little strange, I see nothing wrong with using email for bridal and baby showers, baby announcements, birthday cards, or party invitations. In fact, I think it's genius.
For my baby shower, we designed our own invitation and reminder in Photoshop, then inserted the image in an email. We sent out the invitation a week before the shower, and the reminder the day before the shower, and people could directly RSVP by replying to the email. So simple!
However, if you don't have Photoshop, or don't want to design your own invitation, there are lots of good websites that let you make and send your evites for free, including evite.com, Purpletrail.com, Mypunchbowl.com, and Pingg.com. These do the work for you, sending out all the invitations, sending a reminder, and allowing the guests to RSVP and see other guests who have RSVP'd.
Email is such a good communication resource, and best of all, it's free! So next time your gearing up to buy invitations, envelopes, and several rolls of stamps, think about sending an evite.