
We love our LED lamps (See Five Best Energy Efficient LED Desk Lamps) for energy efficiency, low heat production and for the size of the light bulbs. What we don't love however, is the price (with most costing more than $99). See a couple ideas on making your own after the jump.
LED Panel Light:
Instructables user KresimirPregernik took it upon himself to rebuild an old halogen 12W lamp into a modern LED Panel light, pictured below. Using Plexiglas was used for the panel, drilled for LED foots, and the LED's were also painted with an alcoholic silver paint pen to increase light in the front direction.

LED Hardrive Desk Lamp
The LED Hard drive desk lamp (Pictured above in the top photo) by Instructables user mikedoth turns an old hard drive into a functional LED light. 12 LED's from an old set of Christmas lights were used and the whole unit is powered by an old cell phone charger.
LED Floor Lamp:
Instructables user Torrach turned a halogen floor lamp into a safer, more efficient LED Floor lamp that even uses recycled materials. The steps are involved, so visit Instructables for the how-to.

See also:
DIY: The Best Way To Make Your Own LED Lightbulbs
(Photos: 1st photo the Libra Lamp; 2nd photo LED Hard Desk Lamp from Instructables user Mikedoth; 3rd Photo LED Panel Lamp from Instructables User KresimirPregernik; 4th Photo LED Floor Lamp from Instructables User Torrach)
Comments (3)
If you are going to do this DIY, why not make it to be powered from your phone line? It has ~48V, which is more than plenty for your LED lamp and is free for you!
My two recommendations are to NOT use 5mm LEDs and to look for high CRI emitters.
Devices using multiple small LEDs sound really cool "100 LEDs! Wow!" but in reality aren't very practical. The more emitters you use, the more failures you'll see. It's just simple math. Go into any store that has an old style "Z-bar" desk lamp (66 LEDs! Wow!) and peer underneath; you'll see some burnt out.
Sure you'll need to be aware of heat dissipation and driver issues, but you SHOULD be aware of them anyway if you're serious about lighting. In the end, use fewer emitters, and make sure they're of good quality.
Not using cheap 5mm LEDs also gets around the problem of poor light quality. Cheap white LEDs often have a bluish or purplish cast to them. Also, they almost universally have a very low CRI, meaning that colors don't "look" right under such light. Skin looks pale and zombified, foods look unappetizing, and home furnishings can look lifeless and washed out.
If you want a cheap, low-power light source with decent CRI, check out CCFLs. Instructables has projects that convert the CCFLs from old flatbed scanners into desk lamps. Keep in mind that most "broken" scanners still have usable CCFLs!
In response to the comment posted by adventrising about using the phone line to power a lamp - let me tell you that is not the best idea.
The phone line does supply abound 48 volts and enough current to light a few LEDs - but draw a constant current for too long and the phone company will start looking on your line for shorts - and when they find your lamp etc they aren't going to be very happy - in fact doing things like this might even be in their terms and conditions as a reason to disconnect you.
Considering that LEDs don't use much power anyway, you might as well just power it from a plugpack adapter.