Do you change grip when switching from forehand to backhand and vice versa?

I would say there is no right or wrong answer for this one. I can only say with almost certainty, that there are two conditions where changing grip is not advisable

1. When you are close to the table

2. When the rally is fast. 

When those conditions are met, it will be very uncomfortable (if not impossible) to change grip. 

Other than this (mid or long distance and when the return is slow) , I see a lot of people change their grip from backhand to forehand and vice versa. Usually to,

1. Increase power

2. Increase accuracy of direction of the ball

More or less everyone, including the pros such as Ma Long, change grip sligthly. To add to Pingpongaddicts great answer you can see that many pro-players move up the thumb on the FH-side rubber a bit when hitting a hard back hand.

As Pingpongaddict said 'for increased power'.

@inyagan Do you change grip personally? Changing grip to me bring more benefits in terms of power and comfort but the transition seems to be one that is challenging. Are you only moving the thumb part during the switch?

@elmercasinog I change grip more or less constantly. I think most do but it is different to spot since it goes so fast.
I have service grip when serving FH, I have a loose open grip on short FH-return until last second and then again a slight adjustment for FH-loop. So constanlty small adjustments.

@inyagan Great point. Obviously has to be done subconsciously and probably part of your reflex even with those small adjustments.

Searched some thoughts in YouTube and most of the answers are 'discover what works for you'. Basically, you can choose to or not to. 

Yes, he has many good advices.

When I tutor totally beginners, 6-7 year olds who has never held a bat before, I start with letting them roll the ball to each other on the table using only half the table. If the ball comes to their right side, then use FH, if the ball comes to the left use BH. Rinse repeat.

Don't bounce the ball, just roll.

This so they learn the basics how to hold the racket and switching between FH and BH naturally without thinking. This also learn them to have a relaxed wrist and that they can't change grip to much (or at all) if the pace goes up.

So they need to find a 'default' grip that suits them. (And then develope from there).