Knowing what electronic components you can take on a plane and whether they can be carried on or go in your check luggage can be a task as it can depend on the country and airport you're travelling to and from, so it's a good idea to check with your airline before travelling.
Some basic devices such as hairdryers, straighteners, travel irons and electric shavers can be carried in your hand or hold luggage. Not everything can be put in your checked luggage - particularly anything with a lithium ion battery as there have been cases where they explode!
A good way to avoid TSA officials thinking you have some type of dangerous device is to separate all components in specific boxes. Keep things like LEDS or solder wires apart and the screening staff will know you are carrying parts as opposed to some suspicious device.
“The Transportation Security Administration quite rightly recommends keeping your personal electronics in your carry-on luggage. This not only gives you quick access but makes your electronics much harder to steal. If you do have to put electronics in your checked baggage, secure your bag with a TSA-friendly lock that allows TSA agents into your bag for screening if necessary, but impedes access by others. If you use a non-TSA-approved lock, TSA agents may cut it off as part of the screening process, leaving your bag vulnerable to would-be thieves,” the TSA site notes and provides a deeper list here.
If you have personal items you don’t want to have publicly displayed, the TSA has a notification card you can print out and show to the screener. Items like pacemakers, neurostimulators and insulin pumps are attached to you should be told to the TSA staff and may have you undergo a screening using a millimeter wave scanner or a pat-down instead of going through the metal detector.
Advanced knowledge is key to making sure you are doing the right thing for your specific location and airline. Be prepared and the process becomes much easier.