There are quite a number of factors that go into answering that question. There is the usual requirements - costume, weapons and others things that the system you play in require. But beyond that, there are things you should keep in mind.
First is where will you be playing. Find out what the weather conditions are and dress appropriately. Even with costuming, you can still wear thermals or other layers underneath to stay warm. And realize that when you are out in the wilderness, especially in the mountains, that the temperature can be up to twenty degrees cooler. A good pair of gloves and a scarf will do wonders for staying warm. If you are going to play in high temperatures, perhaps wearing the heavy leather armor should be left behind and a nice, wide brim hat to keep the sun off will be your best friend.
Checking the weather forecast ahead of time will help you to prepare for inclement weather. A wool blanket makes a semi-period cloak to wear over your head to stay dry. Spraying it down with a can of fabric water repellant (such as Scotch Guard) will help as well. It may not go with your costume's look but it will keep you dryer. It is always good to have an extra set of clothing with you - even if the weather is going to be clear. You never know what might get spilled on you during an event.
Next you need to eat. Some groups supply you with the meals but it doesn't hurt to bring along something a bit extra. Something like nuts or even trail bars make a good 'carry along' snack - just in case it takes a little bit longer to clear out those goblins than you expected. You should also carry some form of liquid with you. Water works just fine but you could also add a little flavor to it (water gets boring rather quickly). Try to stay away from anything that requires refridgeration as again you never know how long you'll be away from storage.
If the group doesn't supply any food, you'll have to plan ahead. If you want to go with the minimal amount of requirements, find yourself pre-cooked foods or canned goods that you can eat without heating. Fruits and bread work great but is rarely filling enough for the average person. Canned foods that require heating can have the top lid punctured and then put in a fire to heat. You should make sure that such foods are 'pre-cooked' so that you only have to worry about temperature and not cooking. If you want to go a bit more 'in period', you can find yourself some loaves of bread, cheese, fruits and various cold sausages.
You can also stock a cooler with sandwich meats and bread and keep it at the 'home base' of the event or where you sleep for overnights. Which brings us to the next section.
Sleeping arrangements are often mentioned in overnight games. Some will require you bring your own tent and camping gear. If you have never been camping before, a few things to keep in mind. A sleeping bag is necessary but you'll want something underneath it. Some sort of camping padding to lie on top of will help. In a pinch, you might want to see if your vehicle can be slept in comfortably. If the game supplies cabins and the like, realize that you will more than likely be sharing with people so if such things as snoring or people coming and going all night long would bother you, investing in a small tent should be looked into.
Some overnight games don't have showering facilities. In these cases, a nice wet cloth will help to keep you somewhat presentable, and having a good deoderent will make you appreciated by your fellow players. There are even some sights that don't have any facilities. Check ahead if it isn't mentioned in the game description. A couple gallons of water can be used for washing and you might need to bring a shovel with you to make your own latrine. Be sure to bury what you leave behind. Even if there are facilities, having an extra roll of bathroom tissue is a good idea. You never know if they might run out and, although period, leaves just aren't a very good substitute. If you do have full facilities at your disposal, use them. Keeping clean actually helps you stay awake and focused as well as earning the unmentioned approval of your other players. Don't forget a toothbrush and other daily routines that you normally do at home.
Other items you might want to keep in a bag somewhere are bug repellant, sunscreen, lip balm, first aid kit and, yes, duct tape. Most times, you'll need a pen and a whistle is a great thing to have just in case you get into trouble. Although getting lost may seem unlikely, if you get into trouble, with say a broken leg, using a whistle is much easier than yelling for help.
Now a few things NOT to bring to a LARP. First is illicit drugs. You are still under the laws of the state you are in, and most people would appreciate not being attacked by someone who is under the influence. Next are any real weapons. Although they may look cool, they'll make the rest of the people nervous and you'll probably be asked not to bring them into game. The exception is usually some form of utility/eating knife. Also, explosives, flammables or anything else that might cause damage to you, others or the surrounding environment. Other than that, use your common sense. If you aren't sure, just ask the people running the game.