I found a particular cheap Cree flashlight that lends itself well to being used as a bicycle headlamp if you gang 4 of them up together. This is a really easy one to build.
This light is rated around 280 to 300 "Chinese Lumens", i.e. it's probably in the 200 - 250 lumen range in reality, but that's still pretty bright. It uses 14500 LiPo batteries, which are very close in size to AA cells but are a higher voltage. You can use AA cells but the flashlights will give something more like 100 lumens each if you do.
These are Q5 crees, so be careful that you don't get a dimmer version such as a Q3 because they're sold in identical enclosures. Also these are frequently sold at a discount so Google for coupons or check on sites such as Slickdeals for a good price.
Unfortunately because of the batteries and accompanying charger, the cost of the components is more than the cost of the four flashlights (ie under $30), but if you already have some of those cells and a charger (or just want to get some anyway to try stuff out) then this is a cheap build, otherwise if all you want is a very bright light off the shelf, look around for a good price for a Magicshine of equivalent output, it'll take up less space on your handlebar and won't cost that much extra - maybe $60 total.
This bundle will get hot if you turn on all 4 lights for an extended time and are not actually cycling, which is needed to keep the temperature down due to air flow. However it does have the advantage that you can get an extended run time by simply not turning on all four at once!
Step 1: What You'll Need
Step 2: Remove the Lens
One thing that makes these lights ideal for biking is that the focusable lens can be removed, leaving a wide flood effect rather than a directed spot. In my opinion this is much better for biking at night (although perhaps not, if you are a serious racer who needs to examine the road farther ahead, but in that case you'll be buying a serious light and not making one of these).
The adjustable focus mechanism was by sliding the front of the flashlight forwards or back; since we're no longer using the lens, slide it all the way back now so that there's no obstruction of the light beam.
Step 3: Bind With Zip Ties
Optionally you may want to remove the clips from the flashlights as that may make them easier to bundle together, otherwise you simply need to be careful how you orient the clips when do you the bundling.
Take one of the flashlights and attach the twofish. This is going to be how the bundle is attached to your handlebar. You can save some money on the build by attaching it in some other way, say with velco strips and zip ties. Work out what is best for you.
Hold all four lights together in a diamond shape as in the picture, with the strapped one being one of the pair that are closest to each other, and bind them with zip ties but not completely tight yet. If you're using the clips, slide them underneath the clips. The body shape of these lights makes the positioning of the ties fairly self-evident. Place the bundle face-down on a hard flat surface and push the assembly with the palm of your hand so that all the fronts are perfectly aligned. Tighten and cut as short as possible.
That's pretty much it! You'll be able to open the lights to remove the batteries without cutting the zip ties. (The battery is accessible by unscrewing the clicky switch.)
Step 4: A Word on Charging...
There's always a fire risk with LiPo batteries. I recommend putting the charger in one of these fire-resistant bags while charging, and also unplugging the charger when unattended even if not yet fully charged. Go look at some YouTube videos of LiPo fires and convince yourself that this can be a real danger.
The charger I linked to here has some protection against overcharging as do the batteries but you shouldn't trust it completely.
Many of these chargers are knock-off versions of more trusted brands and may not be built to spec. I noticed with this one for example that the batteries did not give a good contact, and I had to add a rubber band (you can see it in the photos) to make them contact sufficiently.
Note that it lights red when correctly inserted and charging. However it lights green both for fully charged and for not being properly inserted (I mean with a poor contact rather than being reversed). I sympathise with the red/green colour-blind!