Why can't I upload a sketch while other components/devices are connected to my Uno?
The problem is specifically pins 0 and 1. Although they can be used as regular digital IO pins, they also serve as the RX and TX pins for the Uno's serial port. The USB connection (for uploading sketches etc.) is routed to the same pins internally. Unfortunately that means anything connected on pins 0 and 1 can interfere with the serial connection, preventing communication via USB.

In short, it's not necessary to disconnect everything when uploading a sketch. It should only be necessary to disconnect anything from pins 0 and 1. Rather than going through that hassle every time a sketch is uploaded though, it may be best just to avoid using those pins unless necessary (e.g. you run out of other pins, or your project needs a serial connection to another device).