We only used UberX (ok, we took a tuktuk once and got ripped off; never used the metro), so I'd say we had quite a few rides.
We had two suitcases as well as some hand luggage (I think a small cabin trolley, a laptop bag and my gf's handbag). Not an extreme amount of luggage for two weeks in Asia.
As long as we didn't have the suitcases with us, we were fine though.