The most useful Widget (at least in my opinion) is the Text Widget. It doesn't just do text either! It can also do HTML too. This makes it very handy for adding Adsense code, Amazon HTML code or anything else that you feel like. I like to use it to display pictures using HTML image code:

Open the 'Add new Media' by going Media >> Add New.

Then drag the image you want into the Media Uploader. IMPORTANT, the image should be the right width for the sidebar. This is normally about 200 pixels wide, and you can resize pictures using this tool: Shrink Pictures.

Now you're going to need the URL that it gives you, the 'File URL'. You'll also need to take note of the Dimensions, in this case the image is a square (width x height).

Copy that.

Now you'll need to go back to the Widget window and add a Text Widget. Then add the following code. Replace the URL with the File URL you copied as well as the width and the height.

And now you can check out your finished Sidebar!

Lovely!

To make the image a link: You will need to surround the image code with a link code, and this is how you do it:

code for the image goes here

So it will end up looking like this:

And that's how you add an image link to the sidebar!

Of course, you could also use the Image Sidebar Widget (search for Simple Image Widget in Plugins >> Add New.