Rope lighting is inefficient and dim. Look at T4 and T5 fluorescents.

I agree with davidr. Not only is it inefficient, over time the tubes tend to discolor and get pretty ugly.

That makes sense. There was a show on today (Ron Hazelton) that used LED lights but when I looked online they looked really expensive. I was checking on-line at a big box store in the "under cabinet light section"...
What is the difference in these:
Incandescent light wand
Halogen
Xenon
Flourescent

And would any of these be able to be on a dimmer switch? I want to "hard wire" these, not plug them in the wall.

Any suggestions. I have 5 sections on cabinets to do and I'd like to keep the project as affordable as possible.

You pretty much put them in order of inefficiency, with incandescants using the most energy and creating the most heat, and fluorescents using the least. Halogen and Xenon use about 10-20 percent less energy, but considerably more than fluorescent and do put out some heat. Any one of these can be placed on a dimmer, though you will have to get special dimmable bulbs for the fluorescents.

I'm also a big fan of T4 and T5 fluorescents (the number describes how many eighths of and inch it is in diameter, so a T4 bulb is four-eighths, or 1/2 inch). They are very inexpensive, easy to install and to hardwire, with the appropriate accessories, and dirt cheap to run. You can get them in any temp, from cool white to warm, and some are directional, meaning you can either direct them more onto the back splash or on the counter top. Cool to the touch too, which really helps keep the a/c energy bill down.

I find that the BigBox stores have very limited selection when it comes to undercabinet lights. I like Pegasus Associates (see below). They have a great selection, and if you call them they can talk you through everything you will need.

Here is a link that might be useful: Pegasus UC lights

"you will have to get special dimmable bulbs for the fluorescents"

It's not the bulb; it's dimmable ballasts that are special. The "dimmable fluorescent bulbs" we talk about are all CFLs with integrated ballasts. I assume florescent UCs would all use tubular bulbs without integrated ballasts, so it would require a special dimmable fixture, not a dimmable bulb. I'm not sure such an animal is available yet.

Doh! Jon's right. For tube-type it's the ballast that must be rated as dimmable, not the bulb.

They ARE available, though not cheap. Check the link below.

Here is a link that might be useful: Dimmable T5 ballast

We're a bit behind the loop in this department. Dimmable T5 fixtures seem to be available in Europe, but not yet widely distributed (if at all) here.

Multiple switches controlling banks of fixtures are one way to deal with this, though not as easy to use as dimmers.

Rope lights may provide a nice effect in your kitchen, but you may find them a little to dim for 'task' lighting. In my kitchen I have low-voltage halogen puck lights. The low voltage variety uses about 1/2 the energy of a standard incandescent lamp. These must be used in conjunction with a transformer; I would suggest an electronic transformer that can be used with a dimmer. USA Light & Electric, Sunrise lighting and Contractor's Choice lighting are a few companies that carry these items at very affordable prices. However if dimming is not important to you I would strongly suggest a fluorescent fixture.

The low voltage variety uses about 1/2 the energy of a standard incandescent lamp.

Careful, this doesn't mean they are necessarily twice as efficient.

There is a lot of ad-speak in this area. Low voltage is not some kind of magic. For dim lights (say less than 40 watts per lamp), low voltage does allow higher efficiency than line voltage because it allows for a different filament design. BUT, that only applies by comparison to equally dim line voltage lamps.

Fluorescent will always be more efficient than ANY incandescent lamp, at any wattage.