1.) Laptop or Net book (whichever is easier for you) - I have been in situations before where a computer I was working on was the only computer around, and it was having problems. I would think to myself, "It would be really helpful if I could download xyz from the web to troubleshoot this broken PC or backup the system to another drive......" , and I would have to lug the system back to my shop, prolonging the time it takes to fix a problem.
Having a laptop or net book handy can be a real time saver when you are in a pinch.
2.) 6 in 1 screwdriver - This is a must have! I am pretty fond of this model, been using one for years. You can pick one up for around $3-$4 USD online.
Not having a screwdriver in your toolkit is like a surgeon not having a scalpel for a surgery.
3.) Flashlight - Having a good flashlight is also a must have. You may find yourself trying to inspect or work in an area of a computer or network closet that isn't lit very well. There are a couple of types of flashlights, LED flashlights being the best but also considerably more expensive. I recommend a Maglite, they are very durable and carry good warranties. They are also easy to fix.
4.) Phone & Data toolkit - There will be times when you have to make a patch cable or a longer phone cable for someone, and you need a tool to do this on the fly. There will also be times when you have to re-terminate a network jack or test cables. I recommend Paladin brand tools for these jobs. They make all-in-one toolkit bundles that are made up of high quality tools. Try to get a kit that contains cable testers, punch down tools, crimping tools, telephone test set at minimum. Of course, if you are on a shoestring budget, there are cheaper alternatives.
5.) Sharpie & Pencil (and a small notepad) - There will be times you need to mark or draw on something, and having these two (okay, three if you count the notepad) basics are a must have for all computer/network technician tool kits.
6.) Electrical Tape - You never know when you may need to tape a wire that has been stripped back or frayed. This is a necessity if you work with repairing electrical wires inside a computer or other devices.
7.) Small Plastic Storage Box - These are great for carrying small parts such as screws, RJ-11 & RJ-45 jackets, telephone splices, small tools such as hex/allen keys, fuses, etc. The best ones I have found can be located in a retail store that carries fishing supplies.
8.) Band-aids - I can't even begin to stress how important it is to carry a small container of band-aids. Working around computers and networks for as long as I have, I have found that quite a few pieces of equipment can have sharp edges, causing sliced fingers. The next item could have included this as well, but I wanted to list this as a separate item.
9.) Safety Gear - If you ever have to do any data/voice/video implementation work in a construction zone, you will be required to have a hard hat and safety glasses. Some sites I have even been on have required steel toe shoes.
If you have ever seen things done wrong in an old building, new construction work gives you a chance to see or do things how they are supposed to be done. Be sure to not spoil it by getting hurt because you failed to obtain and wear the proper safety gear.
10.) A functional tool tote/case - I have listed a lot of little things here, but where are you going to put all of it? You should carry your tools in a small and functional tote to help you keep everything organized and readily accessible. If you are looking for a good place to pick one up, I recommend visiting your local Lowe's location for one, they have some durable tool totes for a decent price.
Everything I have listed here are things that I find myself using the most. There are other tools that you may like to carry based on what you do. This list is just a starting point. Also, only try to carry exactly what you need, it makes it easier to keep track of and easier to carry.