Are Links pages used anymore?

A doctor wants me to put a links page on his website to other medical institutions. I’m wondering link pages are even used anymore.

If those links lead to sites pertaining to the topic and help the visitor get more information that leads to alternative, progressive information then it’s very useful having a links site.

If the site is about, say, alternative medicine, then it’ll be impossible for one site to cover all topics, so yes, a links page leading to further exploration of a given topic is more than useful.

I use it on my personal website. It’s just a collection of random links I find interestnig. Or perhaps soemone wants to backlink with me. I’ll add it there. It’s mainly just stuff I find relevant to my personal site (which is my hobbies), which in turn, are interesting to my users.

Sure they are. As said, make sure the links are relevant and useful, though. It’s worth giving some information about how clicking the link will benefit the user, too. It can be part of a doctor’s service to provide useful information for patients—but your client doesn’t want people to leave his/her site for no good reason. All kinds of sites link to external sites to provide useful info to clients and customers. (This is supposed to be one of the main ways search engines like Google assess the usefulness and value of sites.)