There is a section in your YouTube creator studio which tells you which songs you can use. Most songs are fine to use as long as you dont monetize. Super big popular songs are usually ok too but they can also make your video not appear to certain countries.
For example if I search Wonderwall by Oasis...
it says... If you use this song Your video won't be viewable in 10 countries: American Samoa, Belgium, Canada, Guam, Luxembourg, Northern Mariana Islands, Puerto Rico, United States, United States Minor Outlying Islands, United States Virgin Islands.
You just have to search and see if the song you want to use is viewable worldwide.
Just go to Creator Studio > Create > Music Policies