Answer
No, your Mojang account will not expire, nor will Minecraft. What could happen is you break the EULA and Mojang revokes your permission to play Minecraft. Or, some servers have a time limit on them; be inactive for too long and your data (on the server) gets deleted.
MOM DELETED HIS MINECRAFT ACCOUNT
Lost My Minecraft Accounts
Do minecraft accounts get deleted?
No, your Mojang account will not expire, nor will Minecraft. What could happen is you break the EULA and Mojang revokes your permission to play Minecraft. Or, some servers have a time limit on them; be inactive for too long and your data (on the server) gets deleted.