People just don't care at all about the ethicity of their bank by now.
I recommend you Cajas (savings banks) before banks in any aspect unless you travel often (they use to be local/regional, but for Caixa and CajaMadrid), and they charge you for withdrawing money in other cajas.
But Internet banks are far better in any active rates, because they have very few or no commisions, and they are suscribed to the major tellar chains that you can use free of charge.
I use Patagon Internet Bank (Banco de Santander Group), but there are others good too, like e-Bankinter. Bankinter itself is pretty good even when you use the non-internet version.
There are other banks that work both on the net and outside like the Popular and BBVA/uno-e. I don't like much the latter one.
If yu are mostly interested in having deposit at small interest rates instead of unexistant interest rates, you can have ING or Patagon.