Skiing is a full-body, high endurance, activity. Being in good cardio-vascular shape is important, and can be achieved through running, swimming, rowing, etc... This can not be over-emphasized. Get your heart in shape.
Assuming you already are in decent shape, here are some exercises that will help you get through those initial days on the hill. I've chosen exercises that require no additional weight -- your body and gravity provide all the resistance you need. (Some can be enhanced by holding light weights if so desired.)
Wall squats: Sit with your back against a wall, your feet together on the ground, and your knees bent at a 90 degree angle. Hold for increasing amounts of time. As strength increases, raise one leg at a time horizontal out in front of you. Repeating multiple reps of 30 seconds to a minute. Feel the burn.
Lunges: Take a large step, dropping your back knee to the ground while bending your front knee (try to keep the front knee at a 90 degree angle). Return to standing, repeat for other leg forward. Do 50 steps or more.
One legged speed squats: Stand with 90% weight on one leg, and 10% on the other. Squat down and stand up as rapidly as you feel comfortable for 20-40 reps. Repeat other side.
Plyometrics: If you are already in good general shape, plyometrics will amp up your legs into bomber ski shape**. Simple moves like:
jump-squats: lower into a squatting position, feet shoulder width apart, then explode up through standing and jump. Return to squat position.
standing three-direction jumps: stand upright, feet together. Jump up, twisting your lower body so your feet now point to the right, but shoulders point forward. Jump back to center, then left. Right -Center -Left -Center -Right. Imagine the snow-flocked pine trees whipping by your face.
High knee jumps (Jump knee-tucks): Stand upright. Keeping your torso at the same height, jump your knees up toward your chest repeatedly. (Legs come up, body stays the same).
Your core is also super-important. Skiing (done right) requires a lot of twisting (shoulders stay pointing downhill while your lower body carves back and forth.)
Crunches, sit-ups, side presses, etc are all super-helpful and common exercises, so I won't explain them. A new one I've added to my repetoire (thanks P90X!) is "Mason Twists" aka Russian Twists: Sit with your back straight and your legs elevated in front of you so your body makes a V feet at chest level. Clasp your hands. Rotate your torso, and hit the ground on the left side with both hands. Rotate your torso to hit the ground on the right side with both hands. Go back and forth, side-to-side for 40-50 reps in rapid succession.
--Balance and static strength--
Skiing is a balance sport. Knowing how your body moves, how it is centered, and how your body responds is important. Consider various yoga moves:
Warrior 1,2 and 3: I won't try to describe them here, since they are easy to do wrong. I recommend seeking a yoga class in your area. But the warriors are GREAT for strengthening your knees (common ski injury areas) and learning balance.
Tree Pose: The ultimate balance posture. In its simplest form, stand with good posture on one leg for as long as you can.
A regular yoga practice will help in all areas of fitness.
**NOTE: Higher-impact exercises like plyometrics can cause injury if done improperly. Land softly when you jump. Do not attempt unless you are in good physical condition. If in doubt, consult a health-care professional.