Let me first say that I would never advocate not hiring a photographer for anyone's wedding. Get pictures! Get lots of pictures! A professional photographer (and I happen to know one, click) will create a portfolio that you will love for years to come.

That being said, photographs can open up that window into the memories of that wonderful day only so much. When all the events during the wedding day are captured on video in real-time as they happen, you experience those events at an emotional level that photographs can never evoke.
You will be able once again to see the joy in each others' faces during your first look and hearing him tell you how beautiful you are as he beholds his bride-to-be for the first time.
Remember, you are the last person in the room when you are a bride so imagine watching as your grandparents are escorted to their seats and seeing the procession of the entire wedding party make their way to the front of the room and being able to experience the anticipation and excitement that takes place just before your grand entrance.
Imagine being able to not only see but hear each of you make your commitment vows to one another as clear and as intimate as the time you said them. The nervousness in his voice and the quiver in yours as the weight of that very moment takes hold.
Watch as the introductions of the wedding party are made at the reception and the introduction of the bride and groom as Mr. and Mrs. for the very first time above thunderous applause.
Watch as the best-man and maid-of-honor share heartfelt stories of your single days or how the two of you met and fell in love. 

For all the moments you didn't see, a videographer will capture those as they unfold. Watch the groom as he opens your gift and hear his voice as he reads the words you so carefully crafted for him. Watch as the guys gather around an iPhone as they try to learn how to tie a bow-tie from a YouTube video. See the reactions of friends and family as they enter the reception hall in all its spender.

These are but a few examples of what a professional videographer will bring you.
Seasoned knowledge of composition, lighting and audio acquisition are essential to the process but the art is in the edit. Your videographer must be a storyteller and be able to tell your story about your day in a beautiful and unique way.

Believe me, I could go on and on, so let me just offer a couple of final thoughts.

By having your wedding captured on video, you are not only giving yourself a gift but you are giving the gift of "your wedding" to those who could not attend and to your future children. Your children will be able to be guests at your wedding. Imagine that. They can see what mom and dad looked like years ago. They can hear what was said throughout that very special day. Your wedding video will be a part of your family that can be passed down as a cherished heirloom.
It could also serve as a living memory for those who have passed on, giving family a chance to see and hear those people once again.

A video is a long-term investment you pay for now and enjoy for many years to come so I encourage you to seek out a professional videographer, whatever your budget. Make that investment. You won't regret it.