Real woodworkers always seem to have a ton of clamps lying around. I'm an amateur woodworker and have neither the storage nor the budget (clamps are expensive!), so I make do with all sorts of weird clamping set-ups. Fortunately, modern wood glue is amazingly strong and applying huge amounts of pressure can actually be counterproductive; Mattias Wandel has demonstrated that the weakest joints are those in which the joint is starved of glue, and the strongest are those with tiny gaps (0.3 mm, ~1/64") filled with glue between the workpieces. So really, clamping is mostly a matter of holding the two pieces of wood firmly adjacent to each other, and letting the glue do the work.
Each step describes different types of makeshift clamp. I've included photos of them in action in each case.
Step 1: Lightweight Spring Clamps
If you're gluing small things, all sorts of household items can act as mini spring clamps. PVC pipe can be cut into C-shapes, and by adjusting the size of the pipe and the thickness of the ring you can change the jaw size and clamping pressure. Binder clips are cheap, come in many different sizes and can apply a lot of pressure. A rat trap is also essentially a spring clamp. Make sure it's clean first, though! (full disclosure: I've never actually used a rat trap as a clamp, so the photo is staged. But I read about the idea in the book Woodworking FAQ by Spike Carlsen, and it gave me the idea to compile this list. So it had to be in here).
Step 2: Caulking Gun
Caulking guns look a lot like a one-handed clamp and work like one, too. Use as-is, or better, with some sacrificial pieces of wood to avoid the jaws marring your workpiece.
Step 3: Tape
Unusually shaped or complex objects can be hard to clamp. Electrical tape is great for this purpose - it's easy to remove and is nice and stretchy. As such, it actively pulls the pieces together (albeit weakly) rather than just holding them adjacent to each other as masking tape does. Masking tape is still handy though.
Step 4: Weights
Provided you can balance them satisfactorily, any source of weight makes for a good way to hold two surfaces together. I've used dumbbells, individual weights, paint cans, stacks of wood, cases of beer, various bottles and buckets and other containers filled with water, or really anything I have to hand. For one long skinny clamping job I even lowered my garage door on to the two workpieces.
Bennybenbenny uses brown paper wrapped bricks as small useful weights in the shop.
Step 5: Stretchy Clamps
Bungee cords work well in some contexts, but you need to take care that the metal ends don't mar any surfaces and they require care when using them (they're dangerous when they release unexpectedly). A personal favorite is rubber surgical tubing - it comes in long lengths, can be applied with differing degrees of force depending on how much you stretch it and how many times you wrap it, and can be tied off just by tucking the end under an earlier loop. On a smaller scale, looping together rubber bands can achieve the same end. And enough rubber bands can explode a watermelon...
Step 6: Tie-downs
Ratcheting tie-downs are particularly powerful and you sometimes have to be careful to not over-tighten them. Use waxed paper to avoid getting glue on your tie-downs, though! I didn't in the pictures shown and had some clean-up to do as a result. Lashing straps(third photo) are inexpensive and effective and I use mine all the time to fix loads to my roofrack. If all you have is rope, try a trucker's hitch.
The fourth picture shows londobali's interesting method of tightening ropes. Toga_Dan suggests using several wraps of cord, then putting a stick through loops at each end, and twisting the stick. This must be a good idea, because it was also suggested by schabanow, callhow and my dad!
Step 7: Pinning
Gluing two surfaces together and then using fasteners to pin the pieces together is not really clamping because the pins are not typically removed afterward. Nonetheless, I include them here because I do this a lot even when the glue is doing the vast majority of the work. For example, using a nailgun allows you to quickly and precisely join two glued surfaces at the cost of a few small (and easily filled) holes in the work surface. The nails themselves have very little strength but the act of driving them in at such speed forces the two pieces together effectively and obviates the need for clamps. It also has the great virtue of allowing you to line up the two pieces perfectly and preventing them slipping (which can be a real problem with wet glue). I like using Miller dowels for the same reason - align and drill everything when dry, then tap together once you've glued it up - no clamps necessary. Pocket holes work similarly to draw the work pieces together, though you need to be sure the resulting ugly holes don't show.
Step 8: Vise
If you have a vise, you also own a handy - albeit fixed - clamp. It has the nice property of having really big jaws. I realize this is a bit of a no-brainer, but I include it here because I often forget this myself - I principally use my vise to hold things while I am working on them with hand tools, and so it doesn't always spring to mind when I'm looking for something to clamp with.
Step 9: Car Jack
A bit of lumber, an overhead beam and a car jack can apply a lot of downward pressure if you don't want to lug weights around. Just make sure everything is lined up well and that you don't overdo it. Remember that a car jack is designed to exert tons (literally) of force and you have Herculean amounts of leverage at your disposal. Distribute this force over the largest area possible by using a big hunk of wood.
You can also use a long narrow piece of wood in the same way - bend it like a bow to exert downward pressure. The third picture came from manxm who used this trick to glue in hardwood skirting boards.
Step 10: Loooooong Clamps
Pipe clamps are great but they're just one more thing to clutter up my 1/3-of-a-garage workshop. So on the rare occasions I need really long clamps, I instead use my one-handed clamps in spreader mode (see last 3 pictures, in case you weren't aware these clamps could do this!) and whatever long lumber is handy. Screw blocks into the 2×4 at such a distance that you can fit the clamp between the block and the workpiece, and tighten. This is unwieldy if you're doing this a lot, but it's fine for the occasional job and has the advantage that the lumber also acts to prevent the clamped material bowing under pressure. Note there is also a commercial product that converts 2×4s into pipe clamps.
Odie Sr.O uses lumber with 3/4 inch holes drilled about 3 inches apart and inserts a dowel where applicable to speed up set-up.
Hopefully this list will give you some ideas next time you need a clamp for a one-off job. My main advice: dry-fit it all together first. That will let you know if your MacGuyver-ed clamping set up is actually up to the task. If it doesn't hold everything in place and close all the gaps, you'll either need to apply more pressure or to cut your gluing surfaces truer.
Runner Up in the
Unusual Uses Challenge
manxm made it!