Tent: If you're going to go on lots of treks, a good tent is a great investment. Otherwise, renting a tent might be the cheaper, lighter & more effective way to go.

Sleeping Bag: A good sleeping bag is a very crucial accessory for the average backpacker, but keep in mind you don't necessarily need the "best ever" sleeping bag there is. Do the research, make sure you understand the climate and the weather you're about to face and then go get the sleeping bag that fits your needs. Usually a bag meant for the range between -5 and -10 degrees Celsius is usually sufficient. 

Big Backpack: This will be your home away from home. Here you will carry most of the weight and your possessions so make sure you try it on first. Many backpacks have different support systems, some are more comfortable than others and the best way of finding it out is to put some stuff in it and walk around with it. Make sure there are no annoying straps that might sore after a few minutes walk and that you feel properly supported.

Knapsack: Will be mainly used for day walks and short treks (1-2 days). A great substitute for carrying your big backpack and as such, also requires a good support system for your back. A very good investment since this is definitely something you can use on a day to day basis, even after you return home.

Headlamp: Makes cooking, reading and basically any night activity outdoors much easier.

Hand flashlight: If you have a headlight, becomes more of a space consumer than a helpful accessory. Leave it at home. 

Gas Cookers: You can either get it on your way or come with it from home, but this is definitely is something you have to have on your trek. Keep in mind sometimes it's not allowed to move gas containers across international borders so sometimes it's cheaper to get it after you've landed. 

Cooking Accessories: When traveling with other people, could be avoided ("I'll take the gas cooker, you take the cookware"), but make sure someone has them. And don't forget some utensils as well.

Pocket Knife: doesn't take up much space and is highly useful. 

Suture Kit: Comes very handy if you tare your cloths, however when traveling in groups, there's usually one more person with a suture kit. If you want to save some room, take some safety pins with you as a temporary solution until you find someone else with a suture kit.

First Aid Kit: Don't go too wild. There are lots of compact basic first aid kits, you can get. Add a few of the basic cold & headache pills and you're set. There's no need to take a whole pharmacy with you.

Locks: Take some small locks to lock your bags.