I routinely receive notifications of obviously spammy Twitter users following me, e.g. accounts with names like @freemoneynow, etc. Is there a danger in allowing them to follow me if I do not follow them back? They could always send me a direct message with a phishing link, but aside from that, is this something I should be aware of? It becomes a maintenance headache if I have to actively prune my list of followers (admittedly not huge, but all it takes is one bad apple).
They can't DM you if you don't follow back.
You can block them if you want to, or you can use one of the many 3rd party services around to do so.
It doesn't really have any effect. It's basically just a number. You'll probably find a lot of them disappear naturally from time to time when Twitter purges spam accounts or they unfollow you because you're not following them back.