It's usually inappropriate. For a blog, the feature I want to see is interesting or useful information presented clearly and efficiently. Adding other stuff usually just elevates the noise floor for no benefit. Ditto for unfocused writing.
The initial "why" is often "I want them to come back to my site" (often contributing to other goals like conversion). You don't need some ridiculous badge system for this. The best and first callback for a blog is good, relevant content and the promise of more.
First, there are third-party "game mechanics" solutions; I think YC even funded one. Second, reposting my own comments:
"Game mechanics" is the new "Web 2.0" as far as misapplied buzzwords go, but "gamification" still comes out of "video games" and "psychology," both of which have been around longer than the web, and the web likes slapping a new term on something and thinking it invented it.
To truly take advantage of game mechanics properly, you really need to know a lot about both video games and psychology. Like anything else, you may have to design with gamification in mind from the get-go, and you'll probably get it wrong the first few times out, which means you'll need to practice (or have betas).
Instead of completely retooling your software or process or "healthcare issue," perhaps instead you can add a meta-game on top: Office Hero was a game added atop Microsoft Word by Lost Garden writer danc: http://www.officelabs.com/ribbonhero && http://www.lostgarden.com/2010/01/ribbon-hero-turns-learning...
You'll never be able to "let's just add badges!" just like you can't "let's use gradients and glossy buttons!" to move the needle.
There's even the notion that video games and traditional UI interaction design are incompatible: IxD is about making things easy, but video games are about intentionally challenging the user. If your users aren't expecting a game, they may end up incredibly frustrated instead.
I did a workshop on adding game mechanics to an existing product (a calendar/dayplanner) and the results varied wildly. One group (Ray and Nicole) integrated social game mechanics into the application really well. Another group (Cecy and Brody) treated each mechanic as a feature, and by the end of the discussion I felt like it was "missing something." You can read the write-up of the workshop here: http://vi.to/workshop/20100426/
My notes include a lot of references, as well as images of the handouts and my own distillation of these principles: http://vi.to/gmnotes
I try to stay away from the term "gamification" because of the stigma associated with it and you're right, it's the new buzz word. But as an avid gamer, I think the achievement/rewards portion of a game can be used across other mediums, like websites, to incentivize visitors and foster discovery of content. I agree that just slapping a badge on a site is a massive FAIL, but providing achievements that drive others to discover interesting content on your site or acknowledge their participation may have some merit.