Electronic Wedding Invitations are perfectly fine for the use in bridal showers, bachelorette parties, rehearsal dinners, save-the-dates, and so forth. However, they might not be as appropriate used for your actual wedding invitations.
Your wedding day is a once in a lifetime event, so putting a little extra effort into the invitations is a good idea. Your wedding invitations give your guests an idea of the formality and style of the wedding, so sending out an e-invitation might give them the impression that you are having a very casual wedding, even though this might not be the case.
Also, think of all of the junk emails you get in your inbox every day! Your electronic invitation could get easily passed up or forgotten about. How many times have you gotten an electronic invitation with intentions to go back later and RSVP, only to forget about it later? An actual paper invitation will most likely be put on a refrigerator, note board, or desk as a reminder of the special event coming up.
My personal issue with electronic invitations is not knowing if the people you are inviting have actually received the invite. Your invite could end up in a junk box or spam folder. Also, after going through the effort of getting the emails, you might get failure notices if the email address was written down or typed in wrong.
Whichever type of invitation you choose, just be sure that the invitation matches the event. If you are having a very casual wedding with just close family and friends, then perhaps a electronic version of an invitation is the right pick for you.