saxophone sound

For me, the sound of the saxophone is the most exciting part of playing the sax. Apparently it shares similarities with the voice, in the way that it is produced and the range of tonal qualities that you can get (eg bright, mellow, edgy). It makes sense to work on this aspect of saxophone playing and there's good advice on the Web to help.

My opinion: your embouchure, throat and tongue position are what really control the sound you make

Air makes the saxophone work. Ideally, there should be a direct flow of air from your stomach / lower lungs through to the saxophone. On the way however, there are a few curves and obstacles, which all collectively influence the sound produced.

The 'shape' of the inside of your throat affects the sound. Tighten up your throat into saying 'eeee' and expect the pitch to rise and volume to drop (your blocking off the airstream, right?). So you want to keep your throat as 'open' as you can, think of yawning and how that feels in your throat. Say 'ahhh' and expect more air to pass through (a good thing). Try to avoid opening and closing your throat to control breathing - keep it open the whole time and use diaphragm / stomach muscles to control airflow.

The position you hold your tongue also affects the sound you make. Keep it arched toward the roof of your mouth. This helps the airstream to 'speed up', giving the sound better projection and necessary for some mouthpieces to actually work properly.

Your embouchure (ie what your doing with your lips and jaw) will affect the sound you make on saxophone. Too tight an embouchure will produce a sharp, pinched sound. Too weak an embouchure, with puffed out cheeks will give a flat, weak sound.

Embouchure
How to form the correct embouchure on saxophone
Mouthpiece placement, tuning
Interesting article about the importance of checking mouthpiece placement and tone control
Mouthpiece Exercises
Shoosie's famous advice about mouthpiece exercises
How to practise Vibrato, with video clip
Advice from Brian Utley about practising vibrato
More mouthpiece advice, with video clip
Brian Utley's good advice on this important concept
Embouchure training
Mr Utley again on embouchure basics
Developing a great sound
Ryan Fraser's advice, under 'Lessons' and 'Getting Started'