That depends on the desired effect. If you would like the wood trim to be highlighted, paint your wall in a contrasting colour. If you wish the wood trim to blend in and be less visible, then matching the colour will achieve that effect, to some degree.
No, you should definately not match wall color to the wood trim unless you want a boring look. It is better to pick a contrasting color to make the trim work stand out. A very popular look is to paint your trim in a white or cream color and use a darker paint color on the wall.
No, the wood trim should accentuate the difference between the wall and another surface. If it's the same color, it'll look too similar and the trim is useless.
the guys in my family tell me it's a terrible idea to paint the trim in my house... with me, if I start i'll do the whole house - french doors, six panel doors, etc. don't know what to do with all this oak trim!!!
Pick wood trim that contrasts and complements the color of your walls. For example, if you have beige walls, moulding and wainscoting will offset the beige nicely and give contrast for the eye. Too much of the same color can be monotonous and make your room look smaller than it actually is.