The love of economy is the root of all virtue.
A Packing List
safety pins, cord, fasteners
Nylon parachute cord ("paracord"), about 5/32" (4mm) in diameter, is easily the most versatile form of rope/cord/string. The very best paracord is MIL-C-5040H certified, but 550 Commercial Type III is less expensive and close to it in quality (unless you actually plan to use it for parachute lines). The even cheaper varieties that are widely available in stores are cheap for good reason; avoid them. Paracord can be easily "disassembled" should you need finer strands — even for sewing and fishing lines. Synthetic cordage frays easily, so take the time to seal any cut ends by heating them (with a flame or stove) to fuse the loose strands together; be careful when doing this, as melted paracord is extremely hot (at least 244°C / 471°F), and will stick to your skin.
I won't even attempt to list the many repair and utility applications for paracord, everything from makeshift carrying handles and fan belts to boot laces and repairing the Hubble Space Telescope (done during the second Space Shuttle mission). When considering uses, bear in mind that paracord stretches under tension (at least 30% before breaking); this is ofttimes a useful quality, but sometimes not. If you'd like to carry paracord on your person for truly emergency situations, it's available woven into bracelets and such; you can also choose to make one yourself, as well as a surprising variety of other items.
Wonder where paracord's "550" designation comes from? It represents its high (550-pound/249kg) breaking strength. The outer sheath, then, can support about 200 pounds, and each of the (usually) seven inner cords about 35 pounds. So if you need a thinner, or less stretchy cord, and a 200-pound breaking strength is sufficient, simply remove the inner cords and use the sheath alone.
In addition to their more conventional uses, safety pins will hold the drapes properly closed in a hotel room, often a prerequisite to getting a good night's sleep (you can also do this with binder clips, or even, in a pinch, the pants clamps found on some clothes hangers, but safety pins are a more compact solution). They will replace missing buttons, provide makeshift zipper pulls, and tack up pant legs for hiking through muddy terrain. Mate one or two with a sarong (or other item of clothing), and you have an excellent emergency sling. Non-rusting stainless steel safety pins also work well as "clothespins", and although I strongly recommend a surgical rubber braid clothesline, the cord & pin solution may offer advantages if you're camping out, and trying to discourage casual pilferage.
Speaking of theft, a handy way to hide valuables in your room is to place them in a sock, safety-pinned into the folds of the draperies, near the top; just be sure not to forget them when you leave! Pinning the zippers of your day pack together will discourage opportunistic thieves, and pinning your trousers pockets closed can help to deter pickpockets in crowded areas (Velcro® is even better for this, if you care to take the trouble).
Other fasteners (pictured at right) in the easily-packed-but-hard-to-find-when-you-need-one category are stout rubber bands (wrap one around each side of a hotel hanger, two inches from the end, to keep slippery garments from falling off), twist-ties (fix broken zipper pulls, necklace clasps, luggage tags), and small binder clips (handy to separate different local currencies, organize brochures / guidebook pages, protect the business end of a disposable razor, and gather together any long straps on items being placed under vehicle seats, to prevent the straps from snagging on things). These contribute negligible bulk and weight, but have the potential to save the day in appropriate situations.
Some will find a pair of bungee cords useful as well, to keep luggage from falling off a cart (or a bus), attach large items to luggage, and/or hold pant legs closed in insect country (the latter can also be accomplished with large rubber bands).
sewing kit, including large needle to accommodate dental floss
You can find such kits in fabric stores (also in the bathrooms of expensive hotels!); most have threads in several colours, and some come with pre-threaded needles. Metal rusts very quickly in humid climates, so don't expect needles to stay sharp for long in such conditions. The serious traveller will think about assembling a small sewing kit, with stainless steel needles (available at ship chandlers), higher quality thread, spare buttons, etc.
My own kit (pictured at left) lives in a watertight plastic "match safe" (intended to keep matches dry, and incorporating a tiny ferrocerium rod — aka "flint" — at the base, for use as an emergency firestarter, plus a tiny signalling mirror in the lid), which you can find at any decent sporting goods store. This is where my stainless safety pins go as well, along with a needle threader, twist-ties, and (before I switched to an LED light) spare bulbs. A 2.4 inch (6cm) length of large diameter plastic drinking straw acts as a spool to hold substantial lengths of my two colours (one light, one dark) of thread; short slits in the straw ends trap the ends of the threads, to keep them from unraveling; needles go inside the straw, and a thimble drapes over the top. Waxed dental floss, incidentally, makes an excellent heavy-duty repair "thread" (for everything from emergency shoelaces to tying the hinge on a pair of spectacles that have lost their screw), so ensure that one of your sewing needles will accommodate it. And needleworkers have discovered that (in the absence of scissors) the cutter on a dental floss box works just as well for regular threads and yarns.
(Ziploc®) plastic bags, garbage bags
The traveller's friend; it's difficult to have too many small, sealable bags. And as mentioned under "rainwear", a couple of heavy duty plastic garbage bags take up almost no space, and can serve a variety of uses (rain/dust covers, picnic blanket, laundry bag, etc.).
repair tape (packing tape? glue?)
I've always been partial to the minimalist school of repair (If it's supposed to move, and it doesn't, spray with WD-40; if it's not supposed to move, and it does, wrap with gaffer tape; if it's more complicated than this, use a Swiss Army knife). I don't carry WD-40 around with me, and my Leatherman tool (which replaced my Swiss Army knife) mostly stays at home these days, but a modest supply of gaffer tape is always close at hand. In addition to wrapping broken things, tape will remove lint, temporarily repair fallen hems, act (with the addition of some tissue) as an emergency bandage, and help seal packages for mailing (though if you're going to be away for a while, it's better to add a small roll of packing tape for mailing packages home).
Repair tapes, however, are not all alike.
Duct tape, of course, is the classic fabric-based "repair-all" tape of American folklore, so much so that books have been written in its honour; you can even make a wallet from the stuff! Also called "duck" tape (which may, in fact, have been its original name), most duct tape is pretty poor quality. You can get good duct tape if you take the trouble to search it out, but it's still somewhat messy to use, and will leave a sticky residue if/when you decide that it's time for it to come off.
Much better, albeit harder to find, is professional gaffer tape, as pictured at right (and which, for good reason, has been used by the technical crews in pretty much every film ever made). It's designed to be torn by hand — in either direction — and still provide very impressive tensile and adhesive strengths. And, unlike duct tape, it will come off cleanly if you need it to. Duct tape is a bit more waterproof, so can't be completely dismissed, but for most repair applications, gaffer tape is the way to go.
Be aware that I am following North American usage here: there is a product called "duct tape" in Australia and New Zealand that is a completely different thing. "Gaffer tape" (aka "gaffers tape"), on the other hand, is as universal as the film industry.
Also note that a discouraging number of people seem to think that gaffer tape is just another name for duct tape: it's not. Unfortunately, though, this means that almost everyone selling "gaffer tape" on eBay is exploiting that confusion by actually selling duct tape (and usually of the typically poor quality)!
You can make mini-rolls of gaffer and duct tape that pack a lot smaller than the big rolls you'll find at the hardware store (this works for packing tape as well, though is a more fussy project). Simply wrap a quantity of tape around a cut-off piece of thin plastic straw or similar (or something you're already carrying, like a cylindrical sewing kit). My preference, though, is to use a square, flat piece of plastic (cut to the width of the tape), the end result being a more rectilinear object that is easier to pack. An expired ATM/credit card is ideal for this.
Gaffer tape also makes a perfectly acceptable substitute for moleskin, an application of which can stop chafing (a common consequence of lots of walking) from turning into a potentially serious problem.
And those travelling with very young children can use gaffer tape for the emergency child-proofing of rooms, by taping up drawers, electrical outlets, etc.
Finally, a non-tape option (though still in the general class of repair adhesives): a small stick of hot melt glue is much more easily carried than tubes of epoxy/acrylic/polyurethane/etc., and can be melted with a match or lighter to provide a strong bond for a variety of repair applications. It also makes for a pilferage-resistant seal, one that (unlike tape) can't be opened and resealed without your knowledge (like old-fashioned wax letter seals).