Supposing for the nonce that God exists, the question:  How can a God who loves people allow them to suffer pain?

The Christian God is a God of love.  He desires companionship with man on an intimate level, where man loves Him and He loves man in return.  Love is a rational choice made by a conscious being.  Love requires a choice: to love or not to love.  A choice requires free will for it to mean anything (if the choice is coerced or forced, it really wasn't a choice, was it?).  Choice of one option permits choice of another option.  In this case, the choice of love has the optional choice of hate (good/evil, etc.).  You ask what kind of God would the Christian God be if He permitted humans to choose hate freely but apparently suppressed his love for humans?  I say what kind of God would force a human to love and claim it's genuine?

One of the better examples I've heard compared the God/man relationship to that of a parent/child.  Does a parent who permits their child to act in an evil manner love that child any less?  This all has to do with the idea of free will and individuals being held accountable to their actions (be it on the mortal or ethereal realm).