"We like you."
Translation:Wir mögen dich.
From what I understand, "You" is the direct object of the sentence. We have to use the Accusative version of you formal since "you" is the noun being used as the direct object. The Dative (which is for indirect objects) of you formal is Ihnen and would therefore be wrong. The last chart on this link helped me understand better. http://german.about.com/library/blcase_sum2.htm
English doesn't make a difference between a normal you and a formal you, but German does. The formal you is "Sie", same pronoun as "her" (but written with a capital S when it refers to the formal you). You'd use it when you want to be polite, for instance with someone you haven't been introduced to yet, a teacher, a mother in law, someone older, etc.
A class speaking to their teacher (1 person) would always say "Wir mögen _Sie."
Informal dich would mostly be used with friends, family or coworkers with whom you are informal.
Btw. The verb for "to speak using 'du' with one another" is "duzen". The formal equivalent is "siezen". Both take the accusative as objects.
Beispiel: "Meine Kollegen und ich, wir duzen uns; aber meinen Chef sieze ich."
Another expression is "per du/Sie sein".
"Meine Kollegen und ich, wir sind per du; aber mit meinem Chef bin ich per Sie."
Mizinamo, We like you. DL says Wir mogen dich. This is from the Formal You lessons. The big question on everyones mind is how did dich transform into a Formal You. I was thinking Ihnen or Sie. I mean WTF? dich isn't even capitalized. Lots ofpeople are giving their opinions and some of them sound pretty convincing as to why dish is a Formal You it just doesn't seem right to me. Lots of conflicting opinions would you please weigh in. I looked for you here in the comments.