It really depends on what your end goal is.
Responsive images are fine, but useless on mobile devices if your original image is not mobile optimized (due to bandwidth/speed limitations on most networks, if not all networks), but you also don't want to be serving a mobile optimized image to desktop users or those with more bandwidth. Some networks will optimize automatically, but this is still hit and mess.
There's a couple of options..
* CloudFlare has some image optimisation as part of their free CDN offering [1]
* Compiling your UI elements/artwork into sprite sheets reduce the number of requests, which can give a dramatic speed increase [2]
* Knowing when to use JPGs vs PNGs (e.g. PNGs for UI elements, JPGs for heavy detail such as photos)
Some things to note;
* In regards to SEO, sprite sheets shouldn't be used for content specific assets, e.g. if you have a page about bridges, and you have 4 images of bridges with filenames which relate to bridges, then you will get a bit higher score. But if you sprite those images, you won't reap the SEO benefits. Hence only use sprite sheets for UI and non content specific artwork.
* Lazy loading high quality images is another approach, e.g. you set the src/background-image to the super low quality version, then lazy load a higher quality one. This approach is questionable, and depends on whether your UI *really* needs artwork immediately in order to function.. and whether it will suffice using a few seconds of lower quality, waiting for the higher quality ones to load. Use with caution, this can get pretty hacky.
* If using responsive design rather than adaptive (there is a difference) [3] [4], then you need to carefully crop your master image to have a "safe zone" which scales accordingly with the layout. The safe zone is the area of the image that you always want to be displayed, everything outside of it being optional context if space permits. If using adaptive, you can crop your images to the specific dimensions required rather than rely on background-position/overflow/background-size trickery, but this is more work. There are also tools which will crop your image on demand [5] [6] but these do not work well with high performance sites and, in my personal opinion, are completely the wrong way to approach asset pipelining.
Gotta cut this post short as I need to run, but hope this helps.
Cal