Joining the national APA won't get you many professional contacts (except for the conference) however, joining your state chapter probably will especially if they have conferences, seminars, etc.
If you join as a grad student it is a good deal, plus you can then attend the conference at the student member rate, which is also a good deal. If you attend the conference you will network with more planners than you can stand! They also offer a job mart and on-site interviews.
Now whether the APA is worth it after you graduate and get a full-time planner job the answer you will get on this board is a resounding NO! That is unless your employer pays for it! They charge a lot of money and all you really get is Planning Magazine and a slew of junk mail begging you to buy books, attend conferences, and join all kinds of APA specialty groups. Oh, and the opportunity to pay even more money to take the AICP test, which raises your annual dues even more.