When you want to get the absolute best results from your photography, you'll need to employ a tripod.
A tripod stabilizes the camera, leading to much sharper images than you're generally likely to get without it. This is especially true when it comes to taking photos in poor light.
Vibration control
These days, many consumer cameras come with built-in vibration control. More expensive cameras may move vibration control to the lens.
Vibration control works by sensing camera shake (caused by your hands when you hold the camera), and moving the lens (or sensor) to compensate.
Vibration control is certainly a good thing, allowing a photographer to capture a sharper image than would otherwise be possible. And without the weight and inconvenience of a tripod.
But vibration control isn't as effective as a good tripod.
Faster shutter speed
You increase your odds of a non-blurry photo when you crank up the shutter speed. This helps counter the effects of camera shake, especially when you're using a telephoto lens.
Of course, higher shutter speeds aren't always available to you. In low-light conditions, you're not going to have that luxury. That's where high ISO comes in.
High ISO
Modern DSLR cameras have the ability to take amazing pictures using higher ISO settings. The resulting images are far cleaner than film (at equivalent ISO settings) used to be.
If your photo requires a high shutter speed (e.g. to capture fast action), the ability to take a clean image at higher ISO settings is essential. If you don't need a high shutter speed (e.g. for a slow moving scene), setting a higher ISO is no match for a tripod.
The tripod is king
There's no getting around it. If you're serious about taking truly spectacular photos, you're going to need a good tripod.
As with many things, you get what you pay for. The basic rule of thumb with tripods, is to get the best you can afford.
