Nerubian Chitins are gathered by Skinners and used by Leatherworkers, and although they show up on a number of mobs, there are only a handful of areas that are actually worth farming.
They sell for around 5g a piece, and Leatherworkers consume them in bunches from one up to 40! In fact, for several levels, the chitins provide some of the best and cheapest leveling options. On the low end, they are used for leg armor enhancement kits, and on the high end, epic gear.
If you can get a group to run Azjol-Nerub with you a few times, with you as the only Skinner, you'll make quite the profit. The skinnable mobs there have an average drop rate of about 25%.
In Icecrown, before you start questing...
Upon entering Icecrown, your first stop will likely be the Argent Vanguard, a mid-size outpost with several quests available to you. Before you begin these quests, or at least, before you hand in A Cold Front Approaches, start farming the mobs around the camp. Once you hand in that quest, you phase out permanently, and all of those spiders will be gone.