Lets see. Different kits require different stuff.It depends on how close to finished the knife is. Something like the 605 designed by darrel, has a handle kit available where all the peices are pre drilled and cut out. Basically all thats left then is finish work so very few tools are required, mostly sandpaper. But if you get into making your own scales from different materials and other steps you need more tools.
I'll try and come up with a list of the basic necessities for your average fixed blade or folder kit. Where the blade, gaurd and pins , or springs etc. in folders are supplied.
A file- rough cut on one side, double cut on the other works well.
It can be used to do rough shaping of handle materials,trimming pins,rough finish of bolsters /gaurd after pins are peened or soldering is done etc.
A drill of some sort with appropriate bits. A drill press is the really the best thing for the job here, especially on folders. You need to be pretty precise on you holes so that everything lines up right. Hand drills will get you by but you'll really have to be careful.
A hacksaw- Most handle materials come in a block thats close to the right size. You'll need to cut it down close enough that you can use the file to make it a good fit. If you start with larger peices of material, you'll probably want something better like a bandsaw to cut it down.
Sandpaper/sanding block- shaping and finishing handle/scales, bolsters, blade. You'll want lots of grits. 80-400 with fairly small steps in between will make the job easier.Start with coarse and get it shaped how you want, remove file marks etc. Progressively move to finer grits removing scratches from previous grit. Smaller steps make this easier. 400 will take a damn long time to remove 80 grit scratches.
A hammer- for peening pins. A nice polished ball peen hammer is great. Any hammer with a smooth polished face will work. You'll need a hard surface to work from for this a vise,anvil or scrap of steel will work.
Epoxy glue- slower curing is better. It gives you more time to work and bonds better. Use it to attach scales in conjunction with pins or screws. Even if it pulls free it will seal the insides of the scales and prevent them from rotting form the inside out.
If you kit uses screws reather than pins for assembly, you'll need the appropriate drivers. Torx are the most common, they can be found at most hardware stores, make sure you know what size to get.
Clamps or a vice- sometimes you'll need more than 2 hands to get the job done. You'll need soemthing to hold stuff in place while the epoxy cures.
Power tools that help, but aren't absolutely necessary:
Bansaw- better for cutting out scales. A scrollsaw will work too depending on the handle material.
Beltsander- takes alot of the work out of shaping things and initial finishing.
Disc sander- Good for porfiling scales.
Drill press- more precise holes. Things will fit up more easily.
Dremel- a million and one uses. Cutting, shaping, finishing
I think thats pretty much it. Hopefully someone else will add to this if they can think of something.