There is no one kind of saxophone. Instead there are different kinds of saxophones - the main two saxophone types are tenor and alto saxophones, but there are also baritone and soprano saxophones. What do all these names mean?
Well, have you ever been in a singing group? If so, you may recognize these terms: a baritone voice is low, a tenor voice is medium-range, an alto voice is medium-high, and a soprano voice is high. The same essentially applies to saxophones: a baritone saxophone plays down low, a tenor saxophone plays in the medium range but slightly on the lower side, an alto saxophone plays in the medium range but on the higher side, and a soprano saxophone plays up high - but there's a little more to it than just that. The following are some complications that exist in all of this:
First, a good saxophone player (now, this means very good!) can play his instrument in such a way that he expands the range of his instrument from the usual range to an additional octave higher. However, few saxophonists can do this to expand the range of their instrument - therefore, generally saxophone players are limited to a fairly small range on their instrument, more like the range of an average singer.
Second, of the four types of saxophones you are likely to encounter in the ordinary world of jazz - baritone, tenor, alto, and soprano - the baritone saxophone musically has more in common with the alto saxophone than the baritone saxophone has in common with the tenor saxophone. Here's why:
When the inventor of saxophones (surprisingly enough, his last name was Sax) decided upon where each of his instruments would be placed in the musical scales, he chose for baritones to be centered around a low Eb note and for alto saxophones to be built using the matching Eb note that is found in a higher frequency (in other words, an octave higher).
Tenor saxophones are centered around the Bb note just below "middle C", which is basically the note at the center of all European music. The soprano saxophone was centered around the Bb note an octave higher.
For these reasons, jazz tenor saxophone players could easily switch to soprano saxophone. For example, John Coltrane did this. This is due to the technique required to play these instruments: since both tenor and soprano saxophones are "Bb instruments" because the Bb note is their center, a tenor saxophone player found playing the soprano saxophone very similar to the tenor saxophone.
The third interesting fact about all these saxophones (and most other instruments as well) is that, the lower you go, the larger the instrument. This is why a baritone saxophone is huge and a soprano saxophone is small by comparison.
Fourth, in most cases, types of saxophones are easy to tell apart. Here's an example of a recording featuring the baritone saxophone:
Two musicians, both playing baritone saxophone. Not exactly high-pitched, is it?
Compare that to a tenor saxophonist in this recording:
Still not a very high-pitched sound, but higher than the first one.
The next is an alto saxophonist. Be a little patient; he doesn't come onto the record immediately:
It's getting higher, but it's not too different from the tenor saxophone. Alto and tenor saxophones are sometimes hard to tell apart.
And, last, for the soprano saxophone. This recording is over ten minutes, so you might not want to listen to the whole thing now, but a short preview should give you the general idea:
Definitely much higher than any of the others. Also, notice from the album cover picture that the soprano saxophone is completely straight, while the baritone, tenor, and alto saxophones are curved into a √ shape.*
So these are the main differences between the instruments. But, coming back to the human voice, what about someone who has a bass voice? There is no "bass saxophone".
Well, actually there is a bass saxophone but it's rarely encountered in music. However, "bass" instruments are sometimes found in jazz: think of bass guitar, or even the acoustic bass; these instruments are used to fill in the lower pitches, making jazz sound more pleasing to the ears than it otherwise would. Low-pitched instruments, like the bass guitar and the acoustic bass, can also provide rhythm or even be used as accompaniment to focus on the main soloist. (In fact, in many jazz recordings the piano is omitted entirely and only the bass is used as musical accompaniment for the soloist, but this is a whole different story.)
Trumpets, by the way, are normally aligned with the tenor saxophone. Like the tenor saxophone, the trumpet is centered around the Bb note found just below middle C.
*This shape comes from http://www.fileformat.info/info/unicode/char/221a/index.htm