I would not say that MagLites are the pinnacle of flashlight development-- that pinnacle has not yet been reached-- but they are definitely way up there. With the rugged functional styling of a Jeep, they go equally well with dirty jeans or a stylish suit. They are waterproof. They are not shockproof by any means-- more than once I've busted a bulb by dropping the things onto a concrete floor-- but quite tough nonetheless. And with that spare bulb in the handle, it doesn't much matter if you do bust a bulb.

Mini-maglites and other little flashlights are nice because you can conceal them quickly. Also it's easy to hold a couble fingers over the lens and let just a little bit of light escape, if you ever need to sneak around. If you're going for a long expedition and don't expect to have to do any social engineering, though, go for a big flashlight. You'll want the light. I carry a big Mag-Lite sometimes; the heft is quite nice.

Headlamps are great. They are basically sine qua non for cavers, and Petzl makes all sort of delightful versions (http://www.petzl.com/). If you do long explorations, a headlamp built into a helmet is really useful. 
Headlamps also leave both hands free for climbing around or taking pictures or whatever. When I go caving in natural caves, I think that a headlamp is essential. But on the other hand, they are fairly expensive and quite obvious ("No, officer, I didn't mean to trespass... I was just wandering around... and, I just coincidentally happened to be wearing this headlamp....")

Speaking of sneaking around, colored gels in red or dark orange can be quite useful. With a red gel, you won't lose your night-adjusted vision. Not a big issue if the place you're in is really dark, but what IS a big deal is that the red light isn't as visible from a long way away. It doesn't make an obvious beam, like the white light. So if you think there might be cops or even just people who would see the regular light from a flashlight-- which is awfull visible-- then use a red gel and you can still see where you're going without being caught. You can buy little five-dollar packages that have a red and yellow gel for the Mini-Maglite. Be warned though, the red gels really cut down a lot on your availible light. You can still see well enough not to walk into any walls, but to really see what around you'll want to go back to white light.

Recent flashlight technology excites me a great deal, because of LED bulbs. They're still awful expensive, but the new generation of flashlights with LED bulbs are bright and will last a long, long time on a single battery set.
For a look at some of the more bad-ass flashlights around-- mostly marketed to emergency personaly and such-- check www.flashlights.com.

Caving tradition (natural caves, that is) says that a spelunker should always carry no less than three sources of light. This is hardly ever so important in man-made spaces, but nonetheless you'd feel pretty damn silly if your light gave out and forced you to feel your way back along the subway track while hoping you don't step on the third rail in the darkness, right? So carry an extra light or two.

But, of course, despite my personal love of flashlights, the type of light source doesn't matter so long as it works. Candles are quite nice if you will be in one area for a while. Paris cataphiles have a thing for carbide headlamps, which makes sense, because the Parisians will go underground for really long expeditions-- like 12 hours at a time-- and the fuel for carbide lamps, smoky and smelly as they are, is a hell of a lot cheaper than batteries. Carbide light is also quite a nice sort of light; it fills up a space with a directionless illumination, and is less harsh than flashlights.

One friend carries a little coleman-style camp lantern. He fills it up with ten cents worth of gasoline and it lights up quite a large area for three hours or so, much cheaper than batteries and easier to deal with than carbide, although it's a pain to carry the lamp. The mantle breaks sometime and the glass shell is delicate, but the light from it is so nice and homey.....

BUT it is considered a weapon if you are caught with it. I don't know where leathermen fit into the picture, and I don't know what blade length makes a knife illegal; I do know, though, that cops who were searching me once took a knife with a 3.5" blade from me and told me that they could arrest me for carrying a concealed weapon; and I know also that if you're arrested for trespassing, a knife in your possession can be considered a weapon and can be the basis for a charge of criminal trespassing, which carries a disproportionaly high punishment. (I was once told by my arresting officer, actually, that possession of an alcoholic beverage when you are arrested for trespassing is ALSO grounds for a criminal trespasssing charge.)
 

When I first got into the idea of vertical gear, I didn't have any rock-climbing equipment. I got some used construction safety equipment, thinking it would be perfect. I found the krabs and lanyards useful, expecially for climbing around scaffolding and such where there are plenty of places to clip in and you just want some added security. The construction-style harnesses, though, are terrible.

A construction-style restraint thing.

Pretty much the same thing but with two krabs. This is really useful if you think you might want to be clipped in occasionally. If you're on scaffolding, say, and you come to a hard part, you can reach up and clip in one... then climb up, clip the second up a bit higher, undo the first... repeat....
It's slow but it really makes me feel much better sometimes to know that I'm clipped in.

A close-up of the two claws. They open much quicker than screw-lock 'biners. The red section next to the smaller one is the shock absorber, so that if you fall the static webbing doesn't cut you in two. I think it just absorbs the shock by letting some of the stitching rip. I'm sure it wouldn't kill you, but it would probably be a lot more painful than a fall on a dynamic rope. I've never fallen on one of them, and never hope to. 

The big hooks are perfect for fitting around small scaffolding struts, or guy-wires on bridges. Unfortunately a lot of scaffolding is just a little too big in diameter, though.

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For rappeling, go for minimilism. An ATC works great for either single or doubled rope. The best way, if your rope is long enough, is to find something you can loop the rope around, slide down the doubled strands, and then pull it down after you. That way you don't have to go up and fetch it and get caught. Be aware that your body weight will sometimes jam the rope in somewhere, though, meaning that you have to go up to retrieve it anyway. 

If you're not sure that you can get back up to retrieve the rope, use a sling. If you have to run, it'll be cheaper to lose a sling than your entire rope. 

If there's any abrasive or sharp extrusions (such as rusted metal-- rust flakes can be very sharp), then think about using a section of chain and some screw-links to make a sling. Then put your rope through a screw-link. I've heard tell that you should NOT clip a 'biner directly into chain, because the soft metal (aluminum) of the 'biner will be slowly ground away against the hard steel of the chain.
For more info and ideas, check rock-climbing info and techniques; check out caver techniques (www.caves.org for the national speleological society); or check out Petr Kazil's page at http://www.euronet.nl/users/kazil. He's played around with a lot of ideas that are useful in an urban environment.
 

Make sure you don't ask your filter to do something it can't, though. If you want to protect yourself from asbestos, make sure you have the right kind of HEPA filter and all that. The little white dust masks are no more than that-- they just protect you a little bit from the dust, not from anything more.

I do not vandalize; my safety is my own concern; and the rules, as far as I'm concerned, can go fuck themselves. The way I figure it, a lock is nice because it keeps other people out, but it becomes irritating as soon as it keeps me out, too.

With all that said, let me make it clear that you should never, ever do anything like cutting a lock, even on an old or abandoned structure. Trespassing is bad; criminal trespassing is much worse; breaking and entering is EXTREMELY illegal and in many cases immoral. DO NOT DO IT. Do not trespass, do not cut locks, do not carry around boltcutters, and don't even think about them.

But in general-- 36" bolt-cutters can go through a lock with a 1/2" shackle; usually they can get up to 3/8", but some locks are harder than others. Remember that the chain or the hasp is often much softer than the hardened steel of the lock shackle itself.
 

Below: A well-equipped explorer demonstrates hip-wader boots and a hand-pumped water-filter. (The tube from the filter goes to a canteen stuck in his boot.) 

And, finally, once you're ready with everything else, remember the importance of STYLE. Nothing screams style like a five-dollar pair of fake oakleys, especially underground.