Here's an example:
This is about 3 or 4 years late, and in my view not a big deal.
It's much better to use the various multi-site "sharing" buttons, so people can share an article with other social media networks as well; all of them include Twitter. E.g., on my blogs I use a "share" button supplied by "AddThis" (See bottom of this post). It accesses almost 300 different social media networks, including Twitter of course.
I've often used the ShareThis buttons, which seem to work just like AddThis, and give you multiple social networks through which to share the article. Also I've noticed that Google's blogger.com has started offering a sharing bar, with several sharing options, including Twitter.
Twitter's button sends you to Twitter only.
Why bother with it? If you want to have something like that on your blog or web site, why not use, instead, the "share" buttons offered by addthis, ShareThis, or blogger.com, or similar products.
Why did Twitter come up with it? I'm guessing they decided it was a good way to try to steer traffic to Twitter and away from other social networking sites. (Also I have it on good authority from @kitchenmage that twitter is using it as another vehicle to promoting lemming-like behavior by suggesting "who to follow".)
The button offers us nothing, except the opportunity to help Twitter build a monopoly and defeat competition.
PS If you know of other products similar to, and as good as, "addthis" and "sharethis", please let me know in the comments section, so I can add them to this post. Personally, I can't see why anyone wouldn't use "addthis". It works fine. If it gives you access to 286 social networking sites, why use a button that only gives access to 6 or 7, or 4 or 5, or -- as in the case of Twitter's button -- only 1? Thanks.
(Short url for this post: http://is.gd/eeELB)