This is meant to be a guide for the sort of things you should look for if you're buying a bike for a woman, whether it's a "women's specific bike" or not. It covers all kinds of bikes, whether for on-road or off-road use.
This is the most important part of buying a bike, as the frame is the heart of the bike. Since it's a big and complicated topic, I've made an article that addresses only this issue, Buying a bike that fits a woman.
One of the main concerns for women is getting the bars closer to them. This can be achieved by both getting the bars futher back (via a shorter stem) and higher up. Getting the bars higher can be accomplished by getting a stem that has an upward slope in the extension part (an old-fashioned quill stem consistes of two parts, the quill that goes down into the steerer tube, and the extension that goes forward and grips your bars; if you have a threadless stem, the entire length of the stem is the extension), getting a stem with a longer quill (if you use a quill stem) or getting a longer steerer tube on your fork (if you have a threadless stem). For information on stems and bars that help with this, see Bodge Your Bike to Fit.
You should also consider the width of your handelbars. For both road and mountain bikes, the width of the handelbars should have some relation to the width of your shoulders. Since women generally have narrower shoulders than men, they shouldn't have the same width bars. I'm 5'5" (medium height for a woman) and I get along pretty well with 23" to 24" MTB bars, and this is using bar ends, which moves the grips in a bit. Many MTB magazines will complain if a bike has bars that are "only" 24" wide, and praise bikes with substantially wider bars. Remember that the reviewers are exclusively men (unless they're reviewing a women's specific bike), so take their comments with a grain of salt. Also keep in mind that I like 24" bars for real technical off-road riding, where wide bars are very useful for meneuvering the bike around tricky bits of track. When I use flat bars on the road, I prefer them narrower. My commuter bike (essentially a hybrid) has 21" bars, which I find perfect. However, before you cut your bars this short, make sure you can fit everything you want on your bars. My commuter bike is a fixed gear, so I didn't have to leave space for shifters!
Many MTBers use "riser bars", handlebars which bend upwards and back a bit away from the stem area. They can be useful for raising the grips up if you can't get the hand position up high enough otherwise, but they have a problem for women: they are usually significantly wider than flat bars. This means that you can end up with bars that are far too wide for you, and you really can't cut off the ends of them, because they curve at the wrong place, preventing from moving your shift and brake levers far enough in. One handlebar which offers quite a bit of rise, but is not too wide is the Juliana handlebar, made by Wylder. It also has a narrower grip area, allowing you to use grips that are either much thinner, or much better padded, than standard grips. However, this thinner grip area prevents you from using bars ends or SRAM twist-shift levers, so if you like these things, you'll have to look elsewhere for a solution.
For road bikes, I find that I am comfy with road bike bars that are 40cm wide (center to center). I think this is wider than the bars many women of my size use, perhaps because I do alot of MTBing. I also like bars that have a short reach and shallow drop, like the Morphe bars mentioned in Bodge Your Bike to Fit.
Another drop handlebar that is very useful is the Terry handlebar, which has indentations to put your hands closer to the brake levers when your hands are on the drops. This is especially useful if you want to use Shimano or Campagnolo integrated shifter/brake levers. These levers put the brake lever even further from the bar than the usual drop bar brake lever, making them more difficult to use from the drops with small hands. I do have quite small hands and have difficuly reaching plain brake levers, and even worse problems reaching integrated shift/brake levers from the drops.
First, see Chris Juden's comments on brake levers. Note that Dia Compe make short-reach brake levers (the BL-24C) for drop bars, but these tends to have more cable friction than brake levers from Campagnolo and Shimano, which compounds the problem that women often have a weaker grip than men. Magura make hydralic rim brakes that with drop bars, which, as Chris points out, help by reducing losses from cable friction and stretching.
Despite the difficulties of reaching the brakes/shifters from the drops, many women still prefer to use Shimano or Campagnolo integrated brake/shift levers because of the convenience of operating them from the brake lever hoods. If you have small hands and want to use these levers, consider getting the Terry handlebars mentioned above. Another thing to consider is that Shimano Sora shift/brake levers have an adjustment screw that brings the levers closer to the bars, which can help. I find that Campagnolo and Shimano shifter/brake lever combination equally easy to use while riding with my hands on the brake lever hoods, and equally difficult to use while riding on the drops. However, the Campag levers are wider when you're riding on the hoods, and some women who have very small hands find the Campag levers pinch nerves in the gap between their thumb and forefinger.
For MTB brake levers, there's little problem, as long as you take advantage of the reach adjustment screw found on your MTB brake levers. Setting these up properly makes it much easier to reach the brake levers.
The place where "women's specific" bits most often show up is in the saddle. However, there is by no means any agreement about what makes an appropriate saddle for a woman. Maybe women find they don't get on with women's saddles at all, and I'm one of these. See my article Bike Saddles for some suggestions, and see Chirs Juden's comments here.
Another very important feature to look for are crank lengths that suit the length of the rider's leg. Some women are quite short, and yet most manufacturers expect them to use the same crank lengths as tall guys, or at best they put 175mm cranks on big bikes and 170mm cranks on small bikes. This is only a 3% difference, for an entire line of bikes with typical sizes for MTBs 16" to 22" (a 38% difference) and for road bikes 49cm to 62cm (a 27% difference). In fact the big bikes ought to have much longer cranks and the smaller ones shorter cranks. See Check your Cranks! for more info.