When it comes to electronics, hypothetically anything can be connected to anything else. The only real barriers are time, cost, and practicality.
Two major things to look out for though are voltage and current requirements.
Most Arduinos operate at 5 volts, so it's often easiest to connect it to other electronic devices which also operate at 5 volts. That certainly doesn't mean you can't connect an Arduino to something that operates at 3.3 volts (for example). However, it means you may need to add some voltage level conversion circuitry (although it's not always necessary, depending on the context).
Regarding current, a critical issue to look out for is how much current something will draw. For example, a motor will often require more current than an Arduino can safely provide. That means you'd need some kind of external power supply which can be switched by the Arduino.
The most valuable thing to do is to learn to find and read datasheets. These give information about electronic components, specifying things like voltage, current, timing and so on. For situations where there's no datasheet available, you may find it useful to learn how to use a multimeter and an oscilloscope to monitor how equipment behaves.