I've been getting these for quite some time, long before I found this forum so I don't think ASF is to blame.
I used to get a few dozen spam emails every day relating mostly to various medical drugs (especially viagra), dating services, various means of enlarging body bits, hair loss treatments, stock picks, real estate, adult services, computer software and so on. Good for a bit of a laugh sometimes but thankfully my ISP installed some software on their servers which has stopped 90% of it. The occasional one still gets through and some of them are for stocks but it hasn't changed much over time.
I would guess that those sending the spam simply have some software which searches for or even guesses email addresses. From the list of email addresses on some of the ones I received I think they must have gone through my ISP's server or used software to guess email addresses with that ISP since they were all similar alphabetically and all to the same server.
I just delete unopened anything which doesn't look like a genuine email. Doesn't take long and not really a problem.
One thing though. I'm certainly not a conservative type but if you have children of an age where you wouldn't allow them to watch "adult" films then I do think that you shouldn't be allowing them to use the internet or email without supervision. Suffice to say that at one point my missus and I were forwarding each other some nice pretty pictures practically every day that you wouldn't want your kids seeing (nothing illegal in the photos but I'm sure you know what I mean). Was good for a bit of a laugh until the novelty wore off (and we got a bit sick of sorting through which were for me and which were for her and vice versa
: ) and now we just press Delete. Not too sure if the family-friendly filtering software works but I seriously do think children should be supervised on the net until they're old enough not to be harmed by such things. I'm not in favour of censorship on the net, I think any form of censorship does far more harm than good, so I have no problem with such things being accessible to adults. But please keep an eye on what the kids are viewing in the same way you would (hopefully) keep an eye on what they watch on TV.