Can you reserve a ride without a cellphone, thus no app?
The Guru Take
Yes, but only with Uber (currently)
Uber currently offers an option to request a car using your web browser. This can be done on your laptop or your mobile browser like Safari, Chrome, and Firefox installed on your smartphones and tablets.
If you are ready, try this link here: https://m.uber.com/
EDIT: Lyft now offers this feature as well.