If you get into MCUs and programmable digital stuff, even at as basic a level as using an Arduino, you also need to be aware that almost invariably whenever you connect your circuit to a desktop PC or to many laptops, no matter whether its via a serial or USB lead or a programmer or debugger, it grounds the 0V rail of your circuit via the PC.
Exceptions that don't introduce a ground: Connections via a USB isolator (which usually limits the max USB speed), Non PoE at both ends RJ45 Ethernet, or
specifically isolated programmer/debugger and USB UART cables.
Grounds introduced via USB are particularly problematic because if you goof and blow up your scope it will almost certainly take out the PC as well, so you've probably doubled the cost of the lesson!
Another thing to be concerned about is ground loop currents. These can become high enough to do damage if there is significant potential difference between supply grounds, or between supply ground and true earth ground.
e.g. if you are working on a radio receiver connected to an external antenna and ground rod, and your mains supply is
TN-C-S, which uses a single conductor for both Ground and Neutral (aka: PEN or CNE conductor) upstream of the customer's utility meter, there can be enough voltage difference at a low enough impedance between your scope grounded to supply ground and the receiver chassis grounded to the ground rod to melt your scope probe leads! Its also very dangerous as you have introduced a non-bonded grounded object into your electrical installation's equipotential zone, and if the PEN conductor gets broken you could get full mains voltage between the chassis of any grounded equipment on your bench and the radio ground. It only takes ONE idiot with a backhoe half a mile away to kill you! If you have a TN-C-S supply, seek qualified expert advice before introducing *ANY* other ground to your bench.
Other ground loop problems can occur due to voltage drops in high current DC circuits. They are rarely dangerous to you, but can be very destructive to equipment.