I actually do use both Alt & Title on nearly every image. I use the Alt tag to serve as a textual placeholder for browsers that either don't support images (some mobile browsing platforms, for example) or have the image display option disabled (to speed up page loads, for example).

I use the Title tag like a caption to be more descriptive of the image because most browsers will display that attribute as a pop-up (or tooltip) when you hover over an image with the cursor.

I got in the habit of doing this to provide a teensy bit more info for my readers, but also for the sake of SEO. I'll admit that this may be a little misguided, however, because I haven't seen anything definitive that the extra info is actually referenced by Google et al. But it's just rote habit now – since my site is nearly all hand-coded, I can whip out basic HTML tags in my sleep!

If you're linking images then the title attribute, if needed, should be on the anchor tag and not the image tag.

I'm sure you don't, but a lot of people either ignore the alt attribute and use the title attribute (very incorrect), or duplicate the content in the alt and title attributes. From an accessibility point of view that's very bad practice. At the end of the day, if the user can see the image then they don't really need the tooltip, if they can't then they see the alternative text.

I've never come across an instance where a title attribute was actually needed on an image (although I'm not saying you never will, but it's a rare thing).