iOS has always come with a built-in Notes app and serves as a pretty easy way to keep basic notes. While some users may prefer something more powerful like Evernote, the Notes app gets the job done for a lot of people, especially since it supports iCloud sync.
If the default font within the Notes app burns your retinas nearly as it does mine, it may deter you from using the Notes app. There's actually a way to change it.
Launch the Settings app from the Home screen of your iPhone or iPad.
Scroll down and tap on Notes.
Here you can switch between three options; the default Noteworthy font, Marker Felt, and Helvetica. Make your selection and then exit.
While Helvetica may be the only acceptable option at this time, it will be a lot easier on the eyes than the default font.