I would say it depends on what it is you are going to offer?
Some companies are on the trashout side, some on the evictions, some on the rehabs, and some that do nearly everything (such as me). Here is what I bring. May be more or less than what others use, as everyone has their own techniques.
Trashouts: Truck, trailer (dump pref), snow shovel, rake, brooms, gloves, mesh net to cover load, straps, and we usually keep some sledge hammers and misc tools in order to break things that are large (such as dog houses).
Janitorial: vac, shop vac, paper towels, oven cleaner (miracle for dirty floors under refer and stove), glass cleaner, pumice stone, glass cleaner, fabuloso, duster, mop, floor cleaner.
Yard: Mower, wacker, brooms, rake, shovel, sheers, pruners, hedgers, and blower.
Rekey: Drill, plenty of bits, two pry bars, locks, lockbox, window locks, slider locks, bolts for the garage door, ladder, CO detectors, and Smoke detectors.
Thats the basic items that we deal with on the initial side (we dont have any wints here in So Cal) We also have the following
Pool pumps, both sump, and reverse suction. Shop vacs for pool drain, and all the chemicals needed to treat the water before draining and after refilling the pool.
2 paint sprayers (graco 695 and backup lts17pro), along with all the drywall items needed, surface prep, and misc items. (my favorite item for this category has become the "Redtail" texture sprayer for matching texture in small amounts)
Plumbing: many different spare parts for 1.25-1.5" ptraps/discharge lines, misc stop valves, 3 different plumbers wrenches, specialty wrenches, misc copper pieces, and items to sweat lines, misc hoses for sinks, pressure tester. (almost all of my plumbing besides very basic is sub'd)
Electrical: Wire nuts, tape, face plates, few lights, meter, plug in receptical tester. (almost all of my elect outside of very basic is sub'd)
Compressor (we have two, one is larger for certain jobs, and one is a small pancake for smaller jobs that need the compressor moved around alot like base/casing.
Generators: We have two, because many houses have no power
Then the obvious as with any other contractor in misc saws, different types of hammers, sized drivers, chizzles, routers, mortising templates to replace doors, bolts and ply for boardups, window glaze, heat gun, and glass cutter for windows (single glaze old windows).
Most important is a good set of subs. Ive got my guys that I need for nearly anything. Carpet, windows, granite, cabinets, plumbing, electrical (although I may start looking for a new one), framing, roofing (especially with roof certs), HVAC.
With your subs, one thing to remember is that with the bank properties, many of the bids are being used to lower the price of the house. So if you know the general cost, then submit a bid yourself and dont have them go to every house. It will burn them out, just as people on the boards are getting burned out on the nationals sending them for misc bids. I will take a ton of pics and send them to the subs and see if they are able to provide me bids based on the pics alone.
If you are trying to do this for a living, dont be the guy out there cutting corners, and using cheap/impropper tools to get a job done. It shows and hurts everyone. I dont work for any nationals, so luckily I havent had the pleasure that some of the people here speak of.