You've got three options, each of which has advantages and disadvantages.
First, the relative reference, eg
"images/picture.jpg" - this is the one that I would usually go for. It means that when you view the page locally on your computer, you get all the images, and it means that you can move files around and as long as the relationships between them stay the same, the links will continue to work without any further action necessary. This is particularly good when images are stored in the same area as the content they are linked from.
Second, the root reference, eg
"/files/images/picture.jpg" - if you keep all images in a centralised location, then depending on what template, CMS or editing system you use, you might find that this is more helpful - it does mean that if you move pages to a different folder or a different point in the hierarchy, the references will still work.
Third, the absolute reference, eg
"http://website.com/files/images/picture.jpg" - this is not generally a good idea unless you are preparing content to be shared across multiple domains. The only advantage I can think of is that if someone saves the page to their computer, it will ensure that all images are referenced if the browser doesn't download them as well. But as others have said, it does increase download time, and is not generally worth doing.