Now that I've started my zombie apocalypse survival pack, I'm adding some of the most important components next: rope, biners and knives. With these three items, the only limit is yourself.
As with most survival packs, Type III paracord is almost certainly the way to go. It has a 550 pound minimum breaking strength and usually seven inner strands. The strength means you can make an emergency harness, hang a hammock or heavy gear, and so on, and the inner core enables you to make a gill net or otherwise use only small amounts of rope as necessary.
I have a 1000' spool of mil-spec 550 cord from Cabelas, though you can save yourself $45 if you go through Amazon. From my spool, I measured out 200' of cord. I considered going with half of that, thinking that the likelihood of an outbreak is low, and I shouldn't commit more rope to a survival pack than necessary. That rope could go to better use for other things around the house. Then I told pragmatic me to shut up. Two hundred feet it is.
Depending on the nature of the rope usage, you may need a biner for securing items, low-friction rope slip (ie, a pulley), or as part of a mechanical purchase. Much of the use I've had is handled quite sufficiently by $0.80 biners from Fleet Farm. Not only are they cheap and small, but they actually have a pretty high weight limit -- often from 400-800 lbs. I'm including a handful of those in my pack, but I will also be picking up two D-shaped non-locking biners from REI. The D-shape helps ensure the load is transferred to its stronger 24kN axis (roughly 5400 lbs of static force).
Also from REI is my Leatherman Surge, rounding out this current set of additions. It's a little heavy and includes things that won't be relevant for zombie survival (eg, screwdriver, bottle opener), and therefore it may be swapped out later for something a little more appropriate. Nonetheless, it's still incredibly useful.
My current collection, now pending the purchase of a few larger carabiners:
Also on the topic of rope and knives, I almost never leave home without my Gerber Shortcut or my homemade paracord bracelet (~9' of 550 cord). Zombies or no, it's just good to be prepared.