Usually in exchange for other perceived advantages? -- Less travel restriction, a more open market for products, potentially ability to look for jobs in other EU countries (but I am not 100% sure about this one).
EU and Eurozone are not linked. What you talk about is joining th EU, which Latvia is already a member of, and which doesn't imply using the Euro as currency.
That's not really true, as all new members are required to start using Euro as a currency.