Formally, 'new' information comes last in a sentence, and 'given' information (understood, or assumed to be understood) comes at the beginning.

So in the sentence 'Я тебя люблю', Я and тебя are both 'given/understood' information, what's important is the 'new' information; 'люблю'.

'Я люблю тебя', on the other hand, answers the question 'кого ты любишь?'

I say 'formally', because it's possible to swap those around for emotive effect, especially in spoken Russian.

But, just to contradict that last sentence (given the subject), this doesn't normally appear to be one of those occassions, since I too have heard 'Я тебя люблю' far more often than 'Я люблю тебя'. In fact, I've even received a gently sarcastic comment from Mrs Scotcher whenever I've used the latter.