In my opinion, ANS is worth the expense. Some companies will fully or partially cover the membership cost. Many companies will support your participation in the various meetings that are held (as either an attendee or as someone giving a presentation). Others will support your participation in ANS governance (the various committees and divisions that put on the meetings, write the ANS standards, etc.). If you're in the Navy and getting out relatively soon, it's a way to get a feel for the nuclear industry (including the parts not related to commercial nuclear power).
Like any organization, what you get out of it is related to what effort you put into it. You can merely read Nuclear News to see what is going on in the industry, you can be heavily involved in your local section, or you can participate in the national organization.
One big benefit of ANS if you are in the engineering area is the opportunity to get to know the various NRC and national lab people involved in your area at the national meetings. For instance, if you are involved in some of the recent Control Room habitability and containment sump issues, attendance at ANS meetings is a chance to meet with the national lab people performing some of the chemical effects experiments. If you are involved in issues with FSAR post-accident containment atmospheric cleanup, ANS membership would let you get to know Dana Powers, whose model is specified in Section 6.5.2 of the NUREG-0800 Standard Review Plan.
Getting involved in any of the many ANS national committees is an excellent way to get to know people in other companies (networking). At one evening event at an ANS national meeting, I was at the same table with the nuclear VPs for two different utilities. One of the discussions at the table was why one utility chose a particular design for their new plant. A different discussion at that same table was with someone who had worked on the Lunar Module before getting into nuclear (complete with stories about the Apollo astronauts).