Readers of my blog know that I am a promoter of Open Science and have been so for a very long time. One of the main reasons why I am, is that Open just is more efficient. No worry about getting formal approval to access something, faster exchange of knowledge, and people just doing their science.
You published your paper and it is appealing to many people. They all start emailing you for a reprint and you end up spending an hour or two every week answering those emails and attaching the PDF to your replies.
Not that you really have time for it, but don't you just wish you had time to print that really interesting paper to put it on your desk pile of papers to read? Well, no luck, your library had to cancel the subscription. And IBL is just a too expensive approach (and sometimes slow).
Now, because the majority of my papers are Open Access, I never have Situation #1. In fact, I don't think anyone gets such emails a lot. (Please leave a comment if you get more than one such request in half a year.) Situation #2 is much more common, though with access to two university libraries, the journals must be really obscure for me not to have access. But there are additional options to solve Situation #2 before you make an author run into Situation #1.
The upcoming solution to this (well, one of them, there are others) is using #icanhazpdf. Just use this hashtag on social media to let people know you really like to read that paper. The screenshot of a Twitter search shows some examples. This is definitely a faster mechanism to have access to reprint papers.
Now, is this legal? No (unless one of the original authors replies by sending a reprint). Do I recommend it? No. See e.g. this post. Is #icanhazpdf part of Open Science? No. It is a symptom of the limitations in scalability of closed-access publishing. With so many people still dying of things that we are so close to curing, I believe scalability is of critical importance.
Therefore, I rather solve this literature access issue by publishing in (true) Open Access journals. You should too; it really is not that expensive (e.g. comparable to one ACS visit and often cheaper). But #icanhazpdf is an interesting trend, one that I feel you should be aware of. And I blog this, because not everyone seems to know this alternative yet.
BTW, another excellent alternative, particularly in The Netherlands. Visit a friend at another university in the afternoon/evening and spend the rest of the day in the library of the other university to copy (download) those interesting papers. The IBL systems will tell you exactly which journals the other university has. Slower, but comes with the advantage of giving you an excuse to visit your friends elsewhere.