As others have stated the main options are fill flash or multi exposure. I thought I'd post this handy example I shot recently where I tried both techniques:

This is the result of using fill flash:

The flash was off camera and to the left, near the ground. I was intentionally trying to get a very dramatic lighting effect, had I used the flash on camera the shadows would be less dramatic and the light more even.

This is the result of two exposures manually merged into one file:

The fill flash shot is more effortlessly natural looking but the multi-exposure (or HDR if you prefer) definitely has more detail and is more striking. It's worth pointing out that whilst I could have done better with the flash I could also have done better with the exposure blending, this is just a quick job to prove a point.

In general the pros and cons of each method are

Fill flash

• + Natural looking
• + Can be done with film
• + Can have movement in the scene
• + Minimal post processing
• - Only works for close subjects
• - You may have to balance the colour of flash with ambient light
• - Can be hard to get even lighting on your subject and avoid shadows
• - Bright backgrounds mean you have to stop down lots or use an ND at you can't use a fast shutter (unless your flash has HSS)

Multi-exposure (HDR)

• + More even lighting, no problems with shadows
• + Striking images
• + Can use any shutter speed
• + Works with all subject, near and far
• - Requires careful post processing to avoid halos, sickening contrast
• - Other photographers will know you used HDR and secretly judge you ;)
• - You can get weird colours in shadows due to secondary reflections.

This last point is worth expanding on. In my example the subject isn't being lit by direct sunlight. So where is the light coming from? Some of it is from other parts of the blue sky (refracting of particles in the upper atmosphere and turning blue), a small amount is bouncing off the clouds (which had almost gone by this point) but a significant amount of it is bouncing off the green grass in front of the subject.

If you boost the shadows too much using HDR, you can get colour shifts, as the shadows by definition aren't lit by direct light, only by light that has already bounced off other surfaces and picked up their colours!