Every time you hit the road in your RV you should carry several items that can be truly called essential. While some essentials are similar to the ones you have at your house some are specific to RV travel.
Basic tool kits: You do not need to haul every tool in your garage with you. However you should have a couple of screwdrivers, large and small adjustable wrenches, pliers, cordless drill motor with bits, small hack saw and even a hammer. Vital to have in every tool box is a roll of duct tape.
Sewer hook-up hoses: You should have a 10 foot and a 20 foot section. Connectors are also a must, and carry a donut for a good seal connection to the campground sewer. Some health departments require the use of a donut type sewer connection.
Chemicals for black water tanks: Proper periodic treatments of the black water tanks of your rig is critical. Be sure that you use treatments that are compatible with septic systems. Some say RV rated toilet paper is required. Others swear that any plain, non-scented or lotion treated paper is safe to use.
Potable water hoses: To connect to the campground water service you must have a food grade (potable) water hose. These will be white in color. We carry two 25 foot hoses. We have needed both on several occasions. Water pressure regulators are highly recommended. Check with your RV parts dealer for the right type of regulator for your rig.
Garden hose: Useful for cleaning the rig or flushing the black water tank. Get a different color from your white potable water hose.
Electrical supplies: Carry blade fuses for replacements as needed. In addition, it is a good idea to have a few replacement bulbs for both interior and exterior lights for your RV. It is also essential to have electrical plug adapters for connecting to shore power. An adapter for 30 amp to 20 amp, 50 to 30 amp, etc. can mean the difference from having power or not. We always use a surge protector as well.
Wheel chocks and leveling blocks: No need to explain these essentials.
Other items that we consider essential: First aid kit, flashlight(s), gloves, and a fire extinguisher.
This list is by no means all inclusive. Each RV type will require specific items for that type of rig. Some like to carry plumbing and electrical repair parts. Your level of confidence in making such repairs will dictate how extensive your on board parts supply will be.