If a derailleur cable snaps on a long ride, how can I keep going?

In the method Pete suggests you don't pick a sprocket as you don't have a horizontal drop out. Go small up font and a middle in the back for chain alignment and pick the best chain length. From there you may need to go up or down one in the rear to get chain tension. Is not going to be perfect. But tension and alignment is more important than the exact gear you want. You can always take out another length so in doubt go longer. And you also lose your front derailleur.

Another possible option if the cable has some length is to knot it around a bolt and bind it in one of the guides. There you have derailleur as a guide and you still have the front.

I have done that ride. That is an excellent ride.

OK now that Pete posted (+1) I don't agree with his answer. I go small upfront (or middle if 3) and the best alignment rear followed by best chain tension.

They certainly are, and you have different alternatives depending on how much cable you where left with and the available tools.

1. If the cable snaps towards the middle of a sleeve-less section (i.e. between cable stops in the frame) you may be able to tie a piece of wire. This will give you some shifting possibilities but don't expect full functionality, since the knots will not be solid as a single piece of cable, so stretching will occur and therefore you'll experiment a sort of "ghost shifting".

2. Another option would be to use the derailleur's limiting screws to hold it on a lower gear. Look your derailleur for a couple of bolt labelled H and L. The H limits the derailleur on the high gear side, preventing it from driving the chain into the frame when the shifter gives all the slack it can give to the cable. Screw that bolt all the way in (but don't make it tight). Depending on the particular derailleur and the length of the bolt you may gain 2 to 3 positions, whether this is suitable for you depends on he trail you want to traverse, your strength and the particular cogs and chainrings on your bike.

3. A third option, provided that you have a way for making a clean cut on the cable is to make a clean end for the piece of cable that comes from the shifter (the "headed" segment of cable) and remove it from the shifter. If your bike uses multiple sections of cable jacket, then use one that is not damaged and is slightly shorter than the piece of cable yo where left with. Remove the "tail" part of the cable from the derailleur. Now assemble the portion of cable that still has a head, the selected piece of cable jacket into the derailleur in some sort of "shifter less" arrangement. That is, the cable head resting against the jacket end. While holding the derailleur manually in position for the gear you want to use, tighten the cable leaving no slack. Fine tune using the derailleur's adjustment barrel. This will leave you with only one useful gear. Tie the remainder for the cable/jacket to the seatstay to keep it from getting tangled.

If the snap happened to close to the head of the cable, then, make a knot on the cable instead. It will be kind of difficult but it is doable.

Options 2 and 3 leave you with only one gear in the rear, but you should still be able to use the front gears.

However: Snapping a cable is very unlikely if the bike is properly maintained and good cable is installed. Even cheap cables are hard to break in normal usage. Always check your bike before taking any trip that will take you far from where you can get help (or a ride home), and perform with enough time to get any necessary spares. Cables and jackets, inner tubes and sim brake pads are cheap enough, so if in doubt, it is better to change them. Spokes can be cheap or very affordable too. If any part of the bike is not in a solid condition and cannot be replaced, it is better to postpone the ride.

"Nothing is so broken you cannot make it worse" - breaking a perfectly good chain in the field, miles from nowhere, with a light weight emergency tool, would be my very last resort.

This will only work if the broken end is not too frayed. Remove the cable completely from the outers and the shifter. Thread the cable though the barrel adjuster on the dérailleur so that shifter end of the cable is butted against the adjuster. Clamp the cable onto the dérailleur (as you normally do, just with a very long tail) with the dérailleur in a compromise position (usually middle of cluster, but towards the big cogs if you have hills to climb, and little cogs if you have lots of flat ground.) Adjust dérailleur with the barrel till its sitting on the chosen cog. Cable tie/tape the remainder of the cable safely out the way (this is really important.....) - its unlikely you have have anything capable of cutting the cable so do not try.

If you cannot thread the cable, you my get away using something else - a cable tie, a piece of string or binding wire may be able to be used - whatever comes to hand.

This will leave you with a 2 or 3 speed bike using the front dérailleur - much better than single speeding it and a lot easier than breaking the chain.

Chain breaking to make a single speed is still an option if these attempts fail.

Edit : Feeling ingenious - if you are lucky and the cable and outers can be reconfigured......
If you have a separate shifter, and the cable is broken close to the dérailleur, you could remove the shifter from the handle bars, and clamp/tape/cable tie it onto the seat post. Rearrange the cable outers, connect the cable back up to the dérailleur, giving you a full range of gears - although shifting won't be as easy.

If the cable breaks at the shifter and you have externally-routed cables, here's what you do:

1. Hand-shift the bike onto a big cog on the rear by pressing on the derailleur as you spin the pedals.
2. Tie the cable around the front cable stay on the downtube.
3. Adjust as necessary to get the bike to hold a gear.

I broke a front derailleur cable at the top of a long climb once, leaving my chain stuck around the little crank for the descent. Luckily, I was able to find a small, flat-ish rock on the side of the road that I could wedge between my frame and derailleur in order to hold the chain up on the big crank. The rock shook free once or twice on the way down the hill, and I had to stop and find a new one, but I was able to get home without totally spinning out my legs.

Here's a quick field repair tip, suggested to me by LBS....

Add an 8-inch cable pigtail to your repair kit. Make one by cutting it from the top end of an old shifter cable (with intact metal fitting on tip). If you're fussy, solder the cut end to prevent fraying in your tool bag. You can scrounge one or two old used cables from your LBS. When needed on the road, remove the broken cable (often breaks within the brifter from fatigue) & any loose cable housings. Thread the pigtail through the last stop above the derailleur and adjust & tighten the cable anchor bolt. Pick a favorite cog setting to get yourself home.

Some answers here inspired me in providing the following solution: source an adjustable brake cable head, something like pictured:

Now, a derailleur cable broken for the first time always leaves you with a part long enough to route it from the derailleur to the nearest cable through-loop. You place the adjustable cable head there and tension the cable so the derailleur stays in the chosen gear.

For the installation tools you need a flat-head screwdriver and the part itself is so small it can literally fit everywhere on your bicycle which makes it really a minimalist solution.

Screw the low and high limit screws in a lot.

Done. You now have a single speed bicycle.