Yes, even on a bright, sunny day. Many times you'll want to use a very small aperture (big f number) to achieve great depth of field. Even on a relatively bright day, your shutter speed may not be fast enough at small apertures to be able to hand hold your shot. Secondly, on a day with tough lighting conditions, you may want to bracket exposure your shot. If you use a very steady tripod, you can use the timer function (or better yet, a cable release) and take 3 exposure shots, and the image won't move even a pixel. This will allow you to later combine the images and vary the opacity at different regions to achieve the "perfect" exposure to the scene. Third, I find that the tripod really makes me a better composer. I take the time to make sure the horizon is straight, the subject is well placed, avoid distracting objects, etc. Oh yes, make sure your tripod is steady. There's no worse feeling than being in front of that perfect scene with your camera on the tripod and noticing that your system is shaking a little bit because of the windy conditions.
2. Carry a cable release.
The timer function on the camera is no substitute for a cable release, BTW. The cable allows you the release the shutter when YOU want to release the shutter, not 2 sec or 10 sec or 15 sec from when you want to release. The release makes it so you don't have to touch the camera at all which will definitely minimize camera shake...especially important for those longer exposure shots. As an aside, if your camera allows it, use the mirror lock up function.
3. Polarizer, neutral density filters, and graduated neutral density filters.
The key to landscape photography is control of light. A polarizer will help take glare off the water and other reflective surfaces like leaves. It also gives some contrast to an otherwise flat, hazy day. A side effect (if you consider it a side effect) is the affect on the sky...will make it a darker shade of blue or even black at higher elevations. Neutral density filters will evenly stop a specified amount of light from hitting your sensor. Let's say you want to get that nice silky effect on a water fall but the day is sunny. If you just shot the image without a ND filter, you might not be able to slow down your shutter speed enough without blowing out the highlights. No problem, ND to the rescue! Grad ND filter is invaluable to the sunrise or sunset shooter. During these "golden hours", the sky is well light but the foreground (e.g., land or water) is not. The grad ND filter is dark on top and clear on bottom and there is a "gradual" transition from the dark to the clear area. Again, these filters come in different strengths. By placing the grad ND filter in front of your lens you decrease the amount of light reaching the sensor from the bright part of the scene (the sky), thereby allowing nice detail from the foreground to show through without blowing out the highlights. There are 2 types of grad ND filters, hard and soft. Hard has an abrupt transition from dark to clear and the soft has a more gentle transition. The hard would be used if you have a very flat horizon, for example like at the Grand Canyon. For an uneven horizon, the soft transition will do nicely. A word of cautions...don't get the screw on type of grad ND filters, as they invariably place the transition right at the center of the lens, exactly where you don't want it. If you're a beginner, I suggest getting a 3 stop hard and a 2 stop soft grad ND filter. All other filters are optional and I'm sure you'll experiment with them once you get these down.
4. Use a hyperfocal distance chart.
Hyperfocal distance is the distance from the end of your lens you should focus at to get the maximum depth of field and still have infinity in focus (for a given f stop and focal distance combination). There are many charts and calculator available on the web. I've made an excel spreadsheet for myself. I always carry this sheet with me in my camera bag.
5. Know the weather conditions before going.
Unless you own a sealed camera like the Nikon F5/D1 or Canon 1D/1V series, you'll want to protect your equipment from rain (perhaps a simple thing like a plastic bag and an umbrella).
6. Landscape = wide-angle lens.
Personal preference, but many will agree with this statement.
7. Remember the 3 elements of a good landscape: foreground, midground, and background.
Try to have something in these positions. This is just a rule of thumb...and you know what they say about rules...
8. If possible, try to avoid shooting in the mid-day.
Lots of harsh light and unflattering shadows around that time.
9. If you have a histogram function on your digital camera, use it!
The LCD often gives inaccurate representation of the exposures. I rely on my histogram, not the little image of the scene I just shot to tell me my proper exposure. As a rule of thumb in digital, shoot for the highlights (as opposed to for the shadows, suggested for film). I'd rather have a slightly underexposed shot than an overexposed one in digital. Underexposed shots are much more easily corrected than an overexposed one.