As others have said, at lower voltages, you need thicker wire to pass high current. Even though a household extension cord can even sometimes power up a toaster or space heater, you won’t get that at 12 volts.
Also, the longer the wire, the thicker it needs to be.
There are six- or maybe eight-foot jumper cables, that are only good for jump-starting cars nose-to-nose, or side-by-side if your battery and their battery are each installed on the near fender. If each battery is on the far fender they might not reach. Forget about these short cables, avoid them.
12-foot, six-gauge cables are great for jumping two cars side by side, even if the batteries are on the far sides of the engine bay, and even if your (or your Good Samaritan’s) driving skills don’t allow to park the cars very close together.
If the dead car is nose-in in a parking lot, it’ll usually have to be pushed out of the space in order to use the 12-foot cables.
20-foot, 4-gauge cables will work in just about any situation, including jump starting another car from behind.
If you’re strong enough to push a car, and/or on a tight budget, get the 6-gauge 12-footers—that’s what I have.
Unless you’re really broke, I wouldn’t bother trying to fix up your old cables. Wal-Mart has several good, inexpensive sets. Places like AutoZone and Pep Boys also have good cables, but tend to charge more.
Also, don’t forget that no matter how good the cable, you need a good connection. Most of the time, the battery terminals on the cars will be rusty, dirty, or corroded. You’ll want to rock the clamps back and forth several times to scratch and clean the surface for a good connection.
P.S. If you do stay with your thin cables, you can make some improvement by letting the “good” car run for several minutes, with all of its accessories turned off, before trying to start the dead car. The dead car’s battery will be at least partially charged, lessening the amount of current you have to pull through the cables during starting.