LED bulbs are the "more better" energy saving answer to the much-maligned "curly" fluorescent lamps. They give a better quality of light, start almost instantly, will work well in lower temperatures and don't contain the small amounts of mercury the fluorescents do. While they are still quite expensive, as with many consumer goods this is changing for the better (and rather quickly too).
As someone who has purchased some of these for use around the home over the last few months, I can give out a few pointers, some of which may be less than obvious.
1 - first, an obvious point: shop around - there are quite a lot of deals and sales. Local utility companies also offer coupons or deals at participating stores.
2 - when comparing the quality/color of light from a bulb, degrees Kelvin (K) is typically used. Look for displays in the store showing the different colors available - a LOWER Kelvin color temperature means a "warmer" color light - 2700K or lower (more like a traditional bulb).
3 - homes in the USA use what is called an A19 fitting for most lamps and ceiling fixtures. When you see all the different shapes and sizes of LED bulbs, it can be easy to miss what kind of fixture it's for.
4 - an LED bulp equivalent to a traditional 60W bulb will have a light output of around 800 lumens - the lamp description will usually tell you what it's roughly equivalent to (40W, 60W, 75W, etc). A 60W equivalent LED lamp will typically use less than 10W, similar to a fluorescent.
5 - if you have a 3-position table lamp, you must use an LED lamp specifically designed for that (they are more expensive). A "regular" LED lamp will not work at all or just flicker on and off rapidly.
6 - good candidates for LEDs are areas where lights are left on for long periods (save money more quickly) and they will work outside, pretty much anywhere a traditional lamp would. The LED lamps have no fragile filaments and so should last much longer in things like garage door openers (where the vibration should not be an issue).
7 - for the above outdoor or utility uses, a "daylight" bulb (with a higher color temperature around 5000K) may give a more pleasing result - they appear brighter, or more "white" or "harsh" if you just need good utilitarian illumination.
8 - for table lamps and ceiling fixtures, the design of the bulb can affect the way the light is produced. LED lamps that have a higher "collar", tend to give a more directional light - more like the cone of a flashlight. Ones with a lower collar produce an area of light more like a traditional lamp - an "all around" sort of illumination. This can make quite a difference, depending on what you kind of lighting effect you are aiming for.