Luggage and baggage charges?
The Guru Take
Nope, not usually. Make sure to get a big enough car
Uber and other rideshare services do not charge luggage. You as a rider need to make sure to order a car that is large enough. The drivers are encouraged to keep their trunks and cargo space clear, so use your best judgement on how much luggage would be appropriate.
If you have many pieces of luggage, perhaps more than what would fit in the trunk, trying order a larger car
For taxis, sometimes the companies do charge for each piece of luggage. Usually, it's only for pieces beyond the first two~.
Tipping for Luggage:
Whether it's a rideshare or a taxi, it's usually customary to tip if there are excessive amount of suitcases and bags, especially if they help you with them!
UPDATE - Relevant thread: How much luggage can I bring in my Uber/Lyft?