When to use IMG vs. CSS background-image?

Proper uses of IMG

1. Use IMG if you intend to have people print your page and you want the image to be included by default. —JayTee
2. Use IMG (with alt text) when the image has an important semantic meaning, such as a warning icon. This ensures that the meaning of the image can be communicated in all user-agents, including screen readers.

Pragmatic uses of IMG

1. Use IMG plus alt attribute if the image is part of the content such as a logo or diagram or person (real person, not stock photo people). —sanchothefat
2. Use IMG if you rely on browser scaling to render an image in proportion to text size.
3. Use IMG for multiple overlay images in IE6.
4. Use IMG with a z-index in order to stretch a background image to fill its entire window.
   Note, this is no longer true with CSS3 background-size; see #6 below.
5. Using img instead of background-image can dramatically improve performance of animations over a background.

When to use CSS background-image

1. Use CSS background images if the image is not part of the content. —sanchothefat
2. Use CSS background images when doing image-replacement of text eg. paragraphs/headers. —sanchothefat
3. Use background-image if you intend to have people print your page and you do not want the image to be included by default. —JayTee
4. Use background-image if you need to improve download times, as with CSS sprites.
5. Use background-image if you need for only a portion of the image to be visible, as with CSS sprites.
6. Use background-image with background-size:cover in order to stretch a background image to fill its entire window.

It's a black and white decision to me. If the image is part of the content such as a logo or diagram or person (real person, not stock photo people) then use the <img /> tag plus alt attribute. For everything else there's CSS background images.

The other time to use CSS background images is when doing image-replacement of text eg. paragraphs/headers.

I'm surprised no one's mentioned this yet: CSS transitions.

You can natively transition a div's background image:

#some_div {
    background-image:url(image_1.jpg);
    -webkit-transition:background-image 0.5s;
    /* Other vendor-prefixed transition properties */
    transition:background-image 0.5s;
}

#some_div:hover {
    background-image:url(image_2.jpg);
}

This saves any kind of JavaScript or jQuery animation to fade an <img/>'s src.

More information about transitions on MDN.

Above answers considers only Design aspect . I am listing it in SEO aspects.

When to use <img />

1. When Your Image need to be indexed by search engine
2. If it has relation to content, including cards (click areas), but not related to design. Design is probably the most difficult thing to parse here because so it's all design right. I would say perhaps functional design (Cards, thumbnails, profile images, things you can click) vs Aesthetic design which is mostly used for sites appeal.
3. List item
4. If your image is not too small ( not iconic images ).
5. Images where you can add alt and title attribute.
6. Images from a webpage which you want to print using print media css

When to use CSS background-image

1. Images Purely Used to Design.
2. No Relation With Content.
3. Small Images which we can play with CSS3.
4. Repeating Images ( In blog author icon , date icon will be repeated for each article etc.,).

As i will use them based on these reasons. These are Good practices of Search Engine Optimization of Images.