Keeping score with algebraic notation is easy! Most 7year olds can do it, and it is required (if you know how) in US Chess Federation (USCF) tournaments. There are many chess equipment sellers who sell scorebooks for ~$3 apiece to keep track of ~ 50 of your games (or just use a blank page).
Advantages of scorekeeping: 1) Replay your games to show better players and learn from your mistakes, 2) Reset positions after illegal move sequences, 3) Prove who is to move and what the position is, and 4) Claim threefold repetition and many other rules that require scoresheet proof. To record a game ("keep score"):
