NO QUIERO ESTAR SIN TI. That's the meaning. If you translate word by word it will have the same meaning, but it will be grammatically incorrect. So the best interpretation for that is NO QUIERO ESTAR SIN TI.
Nunca quiero ser sin ti.
"Nunca podría hacerlo sin ti." It means, "Never could [I] do it without you." In this case, the 'I' is understood from the context.
No quiero que nunca me dejes
Usted nunca ceires separarted de mi -- 'you never want to be apart from me'. Trust me, that is probably the only way to say it--some words in English you can not say exactly in Spanish. Of course there is a way to say it in Spanish and it has nothing to do with the answer before. you say: Yo nunca quiero separarme de ti"
No quiero volver a verte otra vez
To say 'I want bread' in Spanish, you would say 'Yo quiero pan.'
To say 'I want meat' in Spanish, you would say 'Yo quiero carne.'
To say 'I want cereal' in Spanish, you would say 'Yo quiero cereales.'
To say 'I want paper' in Spanish, you would say 'Yo quiero papel.'
To say 'I want a chair' in Spanish, you would say 'Quiero una silla.'
To say 'I want to eat a carrot' in Spanish, you would say 'Yo quiero comer una zanahoria.'
Te amo como nunca, saying before is redundant in spanish. So you basically just sayL I love you like never and the before is implied.