Do search engines pick these up or are they simply tags for the images? Any other advantages to having them?

If they are a good thing, are you best off just repeating the product name?

They are important for SE's and your rank, YES.

Its not a matter of repeating the name over and over, but a blend of KW's and Product name/item etc. goto www.seroundtable.com to read about Keyword Density and get a better idea or how to place KW's on your website.

thats what we do, repeat product name and size. good for accessibility (people with disabilities), and good for search engines!

Yup. That's what I do too. My alt tags, at one point, helped me place high in the serps for product numbers in the thumbnails. It was really quite amazing.

Does anyone put the product price in the alt tag? Obviously it would have to be the sales price (if one) and would need to be changed if the price of the product changed.

I'm trying to put myself in the customers place and wonder it the price by the product description in a search engine would cause me to click on the link?

Any thoughts?