TOOLS
Ok, so most of you will have everything you need already. There's no magic "Gundam" tool out there that's needed. However, just in case you're new to the hobby completely and somehow found your way here let's take just a moment to go over some of the basic tools. Note I mean BASIC. This means enough to get the parts off the runner and put together.
A cutting tool.
These can be a hobby knife or nippers, but I recommend both. While both, you know, cut plastic, they do it differently and it's important to use each according to their strengths. If you HAD to choose one over the other, I would say get the nippers first.
Why? Because though a hobby knife can be used to cut the parts free from the runners, the way they do it—with you putting downward pressure on the runner—can warp or damage the part. Nippers reach in and only apply pressure to the point of contact, reducing the stress on the plastic part nearby.
You can grab a generic X-acto hobby knife or cheap nippers for under $10 USD pretty easily, and in the case of the X-acto they'll last a long time with the occasional refreshing of blades. The nippers, though, I would say if you can, don't skimp. I don't mean break the bank and go buy God Hands, but $20-30 USD for some Tamiya side-cutters or Gundam Planet nippers isn't THAT much more in the grand scheme of things and the leap in quality is noticeable. (I've heard some Xurons are decent, but I've never used one—they seem to be priced between the cheap-os and the Tamiya/GP nippers).
After the nippers, get the hobby knife. They're still useful, especially for some of the nub removal and if you need to alter an ill-fitted piece. Like I said, the price on these doesn't really reflect how well they work, it's the blades that matter. The handle is just what you grip so go with the one that feels best in hand. Myself, I like my Tamiya hobby knife ($10-20 depending on where you get it), but I still have some old X-actos around since they were my first knives.
Sanders
You can get away with no sanders at all if you're really handy with the hobby knife. And for those building their first ever model kit, or the younger crowd, it's entirely acceptable to do no sanding whatsoever. Bandai does a good job of hiding their nubs on the completed kits. But if you want to really make those nubs disappear, you'll need to sand. First, there's the trusty old file:
Seems harsh, or foolish, to take a metal file to a plastic kit, but once we get to the build you'll see why it's a handy tool. Two to four strokes of a metal file on a runner nub and it's gone. Tamiya sells a set for $8-9 that comes with three cross-cut files and they're all you'll ever need. Of course they sell progressively more expensive ones, but if you're just starting out don't break the bank to gain a 2% increase in efficacy (see God Hand nippers vs. Tamiya above).
Next you should get your hands on some sanding sticks. I've tried a few since coming back to the hobby and the Ultimate sanders are splendid:
If you're on a budget, grab at least a thinny stick pack for the white and black sanders. The thin bits are very handy for some of the small spaces you'll be sanding in. Next look for the grey thinny sponge for curved surfaces. Finally, get a hold of the buffer stick. Maybe you've got your own system, and that's cool, but at a minimum make sure you have some high grit (read: very fine) sanders or paper to remove blemishes and nubs.
Tweezers
Get some. At least one pair, something to handle stickers if you're not painting or decals if you've gotten some aftermarket. These don't have to be fancy in any way, just get a size that feels comfortable to use for you. I almost left these in "Optional," but there may come a time when you need to grab a tiny part or pry pieces apart again and it's just nice to have tweezers. And they're cheap. No reason not to have some.
Optional:
Glue
Yes, all Bandai kits are snap-tight. However, not all parts will snap tightly—especially on older kits—and if you're serious about seam removal before painting, it's good to seal up the gaps. Tamiya Extra Thin (TET) is really all you should need, thicker glues are almost never necessary. It's good to have thicker glue, but if you can only get one, get the TET. If you're never going to paint the kit, you might consider skipping glue, but you might run into a detail part that won't stay put sometimes, so it's good to have some nearby.
Panel Liners
These can be enamel liners like Tamiya's, clay washes like Ultimate, and Gundam markers. Gundam kits are loaded with details and lines, and making them pop helps complete the kit. If I had to choose only one, I would grab the Tamiya Panel Liners, one black, one grey. These can be used with or without painting and gloss coats, the bare plastic is perfectly suitable for them. An enamel thinner or mineral spirits (preferred option, in my opinion) can take off excess and slop. Don't use lighter fluid. Just…just don't.
I love the Ultimate washes, but the kits are not smooth surfaces like aircraft and it can be a bit hard to coat and remove the wash. That being said, there are times when they are absolutely useful, so if you don't have some already, make these your number two grab for weathering after painting and a gloss coat.
Gundam Markers, ehhh… Look, I'll be honest here. They're nice, sure, you draw along the panel line and hey presto, a line! However you can save some money by just going to an art supply store, grabbing a fine tip ink pen, and making an enamel wash of your own or using some ink. You can get some black, grey, or whatever color you like for pennies compared to the Gundam Marker sets. Nothing wrong with them, and it certainly saves you the hassle if your hobby shop just has a set there and you have the cash. I'm just saying these fall into the "luxury" category more than the other two.
Enamel washes can be removed with mineral spirits, ink with an eraser—you read that right. If you panel line a "naked" kit, that is, one that isn't painted, wait 10-20 minutes and then use an eraser to rub off the excess ink. This doesn't apply to painted kits with a gloss coat, it's just a funny thing that works ¯\_(ツ)_/¯
Only the ones that need to float like a butterfly and sting like a bee 
. Really found it helpful to someone who knows very little about this subject other than they look cool. Really looking forward to getting started on my Freedom Gundam, Although I've ordered another two so may change my mind when they arrive.