Potato powered coil gun.
For bonus points, make it a rifle and wear a sack of potatoes on your back to power it.

Grappling hook.

Even more bonus points, star in a video "Grif Vs. The World", where you use your crossbow to take out such evildoers as Taterminator and Captain Jack Spud. Obviously, both would have potato-powered weapons.
This suggestion is incredibly silly.

Write a book. That's what I'm doing.

Naw that's not nearly destructive enough, CC.

Alright so to clarify some things: My budget is roughly two hundred dollars, though if it's something interesting enough I might get other people I know to cough up some money as well.

If I make a "crossbow", I was figuring on doing a spring powered lever-drawn locking crossbow. I haven't finalized the design.

Thermite requires me getting the thermite supplies I sold to my chemistry teacher back, but that shouldn't be too hard; I just have to invite him whenever I actually use the thermite. I'm interested in doing the thermite-on-block-of-ice thing, primarily. Though I would also take suggestions, but I've only got about half a pound or so of thermite. (aluminum and iron 3 oxide, if you're interested)

For 'NVG's, I wasn't going to go full-blown actual phototube real NVGs. I was going to cheap out and use IR LEDs and cameras filtered for IR. I'd light up like a halo to anyone with actual NVGs, but naked-eye invisible. Possibly two lenses so I can keep some depth perception.

RC-something was a bit vague, but I was sort of planning on homebuilding something, from potentiometers all the way through the motors themselves. I've got experience with robotics, which sort of transfers, but full-on homebuilding an RC system would be fun/challenging. Depends on how useful the local hobby shops are, though.

Grappling hook: I've got nowhere to use one on. Semi-rural urbanized area, flat terrain, no big huge trees.

Spudguns have always interested me. My initial thoughts on detonation were barbecue lighters, but I'm not sure on that.

So, for a crossbow, something like this?


This is my one, it's less than a foot long, but only just.

The coilgun idea was semi-serious. It's possible to make simple ones from cameras. Then again, it might be counted as a firearm.

RC Can crusher?
RC bottle retriever/sorter?
Roomba?

Semi-auto coil gun. Because everything else in your list is overrated and overdone.

attach sack of thermite to bolt and rig with some sort of ridiculous timer/detonator thing and shoot it at block of ice with crossbow.

I don't think you could pack a decent amount of thermite into a crossbow bolt and still have it be aerodynamic. Unless you make a huge crossbow. But then we'd go into giant siege crossbow territory and I am not really sure how legal it would be to have giant arrow filled with soon to be molten metal.

Crossbow with THERMITE bolts.

If you do the crossbow, weighted roofing nails worked for my bolts.

Thermite shooting crossbow?

Edit:
Oh, and I used weedwhacker line for the bowstring, it seemed to really work.

Actually a coil gun sounds best.
That's something I want to do as well.

RC tunneling robot.

Pick up a bunch of useless skills, that's what I'm doing. Poi, contact juggling, throwing knives, etc. Or you could do something useful, like pick up carpentry. Make some furniture for your future apartment? That's what my first couple paychecks are going to. Coffee table night stands book shelves etc. Writing? Reading? I'm re-reading Dune for like the fifth time