Notebook & Pen - To report any sights or observations.
Maps of the area - When possible
Tape Measure - Helps when drawing a map of sightings in the area
Compass - Can be used as an inexpensive EMF detector & can help if you get lost.
Watch - So that you can accurately report the time of unknowns
Camera w/flash - To take pictures of the area, also good for psychic photos
Swiss Army Knife or Pocket Tool - Can be very helpful in isolated areas
Thermometer - helps in detecting cold spots
Inferred Thermometer - Useful in detecting cold spots in the room while standing in one area.
Flashlight - How else are you going to see in the dark?
Candle Lantern & Candlestick - Flashlights have a nasty tendency to die at the wrong time. Usually right smack dab in the middle of the woods or in a very dark and very cluttered building.
Tape Recorder - To record and unusual activity, and to takes notes for those of us that can't write fast enough.
Camcorder - Just telling people is not enough for most people. So to that end ghost investigators have started using movie equipment and as the technology got better they started using camcorders. Now we use camcorders with inferred night vision technology that has been known to see the ghosts that the naked eye can't.
Cell Phone - In case of emergencies.
EMF (Electro Magnetic Field) meter - Although not absolutely necessary it is helpful in detecting ghost and spirits as it speculated that they give off a strong Electromagnetic field.