For video,
youtube is really easy and well-known and provides easy links.
Video of my dog on YouTube
But for pictures, and videos for that matter, your ISP should provide you some amount of personal webspace to which you can upload and share. That would be my first option.
But there are tons of photo-hosting sites out there - I don't use them but some people do.
Photobucket,
Picturetrail, etc... I can't pro or con any of them any of those since I don't use them. The only thing you have to watch out for is if they prevent hotlinking (meaning the picture is hosted on their site but will not be allowed to be displayed elsewhere).