For anybody unfamiliar with Europe, I just want to add that there aren't any checkpoints or border crossings, you just drive through or walk over. Half the time you won't even notice you're doing it. You're just supposed to have your ID on your person when you do.
Ireland (and previously the UK) is the only major exception to this, as it's part of the common travel area alongside the UK. In practice, this doesn't make a huge difference when you're an Irish or EU citizen (it does if you're a tourist who needs a different visa to visit), as it's an island, and airlines require a form of ID to board anyway. When travelling from Ireland to Schengen, I usually have a passport in my carry on luggage as a backup, and take my passport-card (similar to a national ID card) in my wallet.
