Your best
choice, if you can get it, is light set with a full DC power supply. A simple
direct current (DC) power supply can be made with a bridge rectifier and a smoothing
capacitor. The rectifier plus the capacitor converts the alternating current (AC) waveform
from the plug in your wall into a slightly wobbly DC voltage. LEDs were designed to run on
DC (not AC!), so they light up nicely.
How can you tell if a set has a DC power supply? They have to put the rectifier and capacitor somewhere. Most of the sets I've found use a small box with six wires shortly after the plug for that. Two wires are AC in, two are AC to the plug at the very end of the cable and two are 168 VDC to the lights along the string. If you see that box, you're looking at a set with a DC power supply.
Blinker LEDs need a DC power supply so if you find a set with some bulbs that blink, you'll find the box. You may also run across "multifunction" lights. These have a DC power supply in a different shape with a button to select the function.
I haven't found a brand where I like everything about them, but the 70 LED Martha Stewart Living C9 Icicle set from Home Depot has a DC power supply in 2010.
The second best choice
is a full-wave rectified set without a smoothing capacitor. These use two sets of two
diodes, one set at each end of the light string, to implement the equivalent of a bridge
rectifier. They flicker 120 times a second, but your eye can't perceive something turning
on and off that fast so it just sees solid light. Because both the starting and ending
plug contain doides and a resistor, they tend to be extra large as shown.
Because they're fully rectified, the voltage which reaches the LEDs does not alternate from forward to reverse (positive to negative). LED's burn out when too much reverse voltage is applied, so a full wave set should last much longer than a half-wave set.
I really like the Ecosmart commercial grade LED lights from Home Depot. They're a full wave set and unlike every other set I've tested, the screw-on bulb assembly is weather-tight, making them suitable for use outdoors without the steel leads rusting. The GE Energy Smart lights from K-Mart and the identical box in a different color Martha Stewart Living lights from Home Depot are also full-wave sets from the same manufacturer which give off a pleasant light but they aren't weather-tight. I gave GE sets to friends for Christmas in 2009 and folks loved them.
The worst choice is a half-wave set. Half wave sets only light on one half of the AC wave form. They flicker 60 times per second and are only on about one third of the time. I perceive this as flickering whenever they're at the corner of my vision but more or less solid when I look at them straight on. Your exact experience may vary. Half-wave sets have an additional problem: LEDs burn out quickly if driven with current in the wrong direction. A fully rectified set uses diodes designed to stop 120 VAC reverse current but half-wave sets use the combined LEDs themselves to enforce directionality. LEDs are not designed to deal with this, so they leak. Over time, this causes them to burn out sooner than they would with DC voltage from a power supply.
If there's no six-wire box and only the normal small christmas light plug, you're looking at a half-wave set. These can be nice (and cheap) as raw materials for hacking, but otherwise stay away.