What can I do for my baby to not become a cry baby?

Accept and nurture. Babies cry to get basic needs met early & later cry in tantrums & responding to negative events.Nurturing does not create a cry baby.The kid who stubs his toe will cry loud & briefly, settle & return to play. The parent who tells him to stop crying invalidates his decision that it hurt & degrades his self worth.Try to strike a balance accepting the valid cry & rejecting the self indulgent whining.
Encourage Expression. It's important to encourage your child to express his feelings. However, teaching the proper tone of voice is important. Ignore requests made in a "whiney" voice. You may need to make a brief statement - "i can't hear whine!" - to make your point. Always important that you model correct conversation. Kids emulate the adults in their world.
Encourage language. Once your baby begins to talk/reaches pre-school age, one of the best things to do is to encourage their language development and to express their feelings. Pre-school kids who are "whiny" tend to be so because they feel they cannot adequately express themselves, get frustrated, and resort to crying/tantrums. When this does happen however, don't negotiate with them, be firm and decisive.