Okay, I was recently asked to teach bass and so I wanted to come up with some useful exercises.
Here is the result.  These exercises are really simple but can be challenging, as they make you
think about your fingers.

Note: this can be played anywhere on the fingerboard.  use all four fingers,
and only use one finger for each fret... NO CROSS-OVERS!

Here is the basic exercise
G|-------------------------1-2-3-4-|-4-3-2-1-------------------------|
D|-----------------1-2-3-4---------|---------4-3-2-1-----------------|
A|---------1-2-3-4-----------------|-----------------4-3-2-1---------|
E|-1-2-3-4-------------------------|-------------------------4-3-2-1-|


Easy enough.  You play it once, then play it backwards.
Now you repeat this again, but with a twist:  You start with your second finger.
So the next stage would look like this:

G|-------------------------2-1-3-4-|-4-3-1-2-------------------------|
D|-----------------2-1-3-4---------|---------4-3-1-2-----------------|
A|---------2-1-3-4-----------------|-----------------4-3-1-2---------|
E|-2-1-3-4-------------------------|-------------------------4-3-1-2-|


As you may have guessed, for the next stage you start with your third finger.  (I find this to be the most difficult.)

G|-------------------------3-1-2-4-|-4-2-1-3-------------------------|
D|-----------------3-1-2-4---------|---------4-2-1-3-----------------|
A|---------3-1-2-4-----------------|-----------------4-2-1-3---------|
E|-3-1-2-4-------------------------|-------------------------4-2-1-3-|

And here is the fourth and final stage.

G|-------------------------4-1-2-3-|-3-2-1-4-------------------------|
D|-----------------4-1-2-3---------|---------3-2-1-4-----------------|
A|---------4-1-2-3-----------------|-----------------3-2-1-4---------|
E|-4-1-2-3-------------------------|-------------------------3-2-1-4-|

Have fun.  I hope this helps some beginning bassists.
-Andy (stuperandy@hotmail.com)

Please leave a little feedback if you find these to be helpful.