Actually, Technora, Vectran, Dyneema, and the like have stretch characteristics pretty close to those of wire rope. Half a percent elongation at 25% breaking strength, versus 10% for polyester and up to 30% for nylon. You should not use them in applications where hard dynamic loads may be expected, including mainsheets, unless you want to blow up blocks or snap your boom. Halyards, reefing lines, and standing rigging: they are fabulous for that. When we buy our big boat, I plan to replace all the stays with synthetic line. Stronger than steel at one-seventh the weight -- you can save 40-50 lbs aloft on a stoutly-rigged boat.
I think most cable failures stem from fatigue and corrosion. Our keel cables make a 180 turn and a 90 degree turn around ~1" radius sheaves, then suffer multiple turns around the winch drum. Cycle that a few hundred times, add the weakening effects of internal corrosion, and you have an accident waiting to happen. Synthetic line has become favored for winching applications because it doesn't rust and it doesn't easily fatigue. But it does have its own issues. Uncovered aramid cordage can lose substantial strength with intense UV exposure; and while it's a devil to cut while splicing, it will part easily when under high tension if it contacts a sharp edge. That's two reasons the powers that be are still leery of its use for lifelines.
My recommendation for anyone considering a synthetic winch line would be 3/16" Amsteel Blue (a 12-strand, HDPE line with 5400 lbs breaking strength) with (optional) an inexpensive polyester sheath pulled over it to make a sub-1/4" line. You can buy a similar combo ready made, or you can make your own by stripping the cover off a double-braid polyester line. The core will carry all the load. In fact, you can buy ATV winch lines already eye-spliced with a thimble for the bitter end (they sell 12' lengths for ATV snowplow blades):
http://motors.shop.ebay.com/i.html?_fro ... etic+Winch
http://cgi.ebay.com/ebaymotors/Syntheti ... 4cf7a24f7a
Or buy by the foot at Redden Marine, who have the best prices & service around:
http://www.reddenmarine.com/marine-supp ... -blue.html
The stuff is laughably easy to splice. Whether using naked Amsteel or covered, I'd advise leaving a good 5-6 turns around the winch at keel-full-down. That's good policy whether your winch cable is rope or wire. Replacing the keel cable was the very first improvement we made on this boat. After three seasons of use, often raising and lowering the keel as many as four times a day, the cord looks good as new.