The reasons people like them so much are obvious. They make a page more visually interesting, as well as containing lots of useful information that can be easily and quickly processed by the visitor.
I've never created any infographics myself, but it doesn't seem all that hard to do. And you can find the raw data to inform and organize your images in many places on the web.
Their use by bloggers and other web publishers could have peaked, however. When infographics are being used to explain why you should use them, it's clear that the method is on the verge of over-saturation!
Also, while the backlinks that they generate do have definite SEO benefits these days, it looks like Google may well be discounting their value in the future.
That said, there's nothing inherently wrong with them. I doubt they could do any SEO harm, and they certainly have a lot going for them in other areas.
As yet, I haven't published any ones that I've found elsewhere on this site and probably never will. One reason for this is that I want to maintain the blog's look and feel. I'd prefer to keep it clean and basic in design and focus on the verbal content.
Traditional blog posts are not nearly as eye catching as those containing infographics, of course. But you can still give them some visual impact by using bullet points, bold text and italics, etc. And of course you can describe all the same information contained in an infographic.
Better still, you can simultaneously investigate and interpret the information in an insightful and comprehensive way. While people do tend to have much shorter attention spans these days a certain proportion of your visitors will appreciate this more old fashioned approach.