Is praying for non-Muslims permissible in Islam?

Can a Muslim pray for a non Muslim? As far as I know when a Muslim sneezes if someone tells him "Yarhamkom Allah" he can reply by saying "Yahdekom Allah wa yosleh balakom" to him. Are some prayers not allowed for non Muslims? Can I pray that God guides him to Islam, but can't ask God to forgive him? What about normal prayers like wishing him to pass an exam or wishing him good health?