I've been asked this question a couple of times recently and my answer is always the same...No, rats do not need a bath. But there are a couple of exceptions to this rule.
1. Older rats can lose the ability to clean themselves as they get older and may urinate where they sleep instead of getting up and going over to the potty corner of the cage. A rat with hide Leg Degeneration will also need help keeping clean and in these cases you may have to bathe your rat.
2. If you let your rat on the floor for free range time, meaning you have rat proofed your room and you let them run around to get exercise but they find a dust ball and roll in it and get dirty. In this case you can either take a baby wipe and clean them off with that or you give them a bath.
Some rats like water and some do not.
When giving your rat a bath they may do what I call a stress poop, meaning they start pooping in the water. Just take a paper towel and scoop the poo out of the water and finish your bath. You should only put enough water in the bottom of the tub so that it reaches just above the legs of your rat and their belly is just touching the water. You don't want the water to be very deep that way it doesn't scare the rats too much if they don't like water.
Use a shampoo for rats or you can use Dawn. Most times though just using water is enough unless they are really dirty/stinky. Using shampoo or detergent can dry their skin out so you don't want to bathe them unless you have to. Never use a flea and tick shampoo because of the harmful chemicals they contain.
Don't make your rat stay in the water for too long and wrap them in a fluffy clean towel and let them snuggle with you afterwards. Don't forget to give them a treat like a yogie to reinforce this being a positive experience.