Forum Moderators: open
As far as negatively affect you... unlikely, but the link provided to you is only providing potential visitation and no PageRank.
There is always a chance that the webmaster/site owner is attempting to manipulate PageRank so that only their own pages benefit, but this can also be just "no common knowledge".
Another example of just "bad design" - a friend had me look at his site to provide feedback. The entire site was JavaScript -links and everything which Googlebot can not read, thus Google would only (possibly) see a single page.
I am fast going off reciprocal links for this very reason. Monitoring all of these cowboys takes too much time.
Provide good content and some sites will give you a one way link because of it. Give one way links yourself to other sites that complement yours and all will be well in both the eyes of Google and your visitors :)
Is it possible that I might suffer somehow? I have placed a link to them on my links page. Should I get rid?
Even if their links page was penalized you wouldn't have anything to worry about... unless you are linking to that specific page.
I'm assuming that you've linked to their home page and not their links page?
If so, the only thing you need to worry about is whether this is a dodgy link partner who is intentionally blocking any PR benefit to you by making their links page unindexable.
(Pretty sure "unindexable" isn't a word, but you get the point. lol ;))