There is a fantastic set of parenting courses aimed at teaching parents very basic child psyhcology - I did both and highly recommend them. They are called "You make the difference" and "Raising Secure Children". They were written by some American psychologists (can't remember who sorry) but you shoud be able to find info easily enough. If not let me know and I'll try to fin my info.
Despite what many many supposed experts and parents who have been there etc will tell you - ignoring a child's feelings is dangerous (not to mention downright rude).
Ignoring them because they are whinging tells them you don't care. They don't stop whinging because it's the wrong thing to do and they don't stop because they have learned there are better ways to communicate.
They stop whinging because they have been taught that expressing their feelings is pointless, unappreciated and unheard.
You may get the "desired result" - that being that they stop whinging and clinging, but in the meantime you have taught them that at times when their feelings are overwhelming them and they can't get their words out or express themselves through actions or communicate their thoughts in some magic manner that you aren't interested. This is a dangerous set up for a relationship that has many years ahead that are very likely to have more trying times than the clinging.
If you read up a little on basic child psych you'll understand why all the myths about spoiling children and giving in to children etc are wrong.
But to try and put it in a nutshell....
Children experience their feelings as a physical experience at first and through time and our guidance learn understanding and then to associate this with labels/words/signs. For instance "this horrible dry feeling in my throat means I need a drink" and soon instead of crying they say "drink". Or like lizaveta's little one has learned to express that she is scared because of a dog - which may I say is exceptional communication of feelings for such a little one.
They are not born understanding their feelings. So sometimes the reason they are whinging is because they don't have the words, they are having big feelings or desires that they can't express and the longer they experience the feeling for the more desperate they get and the more difficult it becomes for them to express themselves.
Think about how you feel when you are overwhelmed with emotion and then imagine how that would feel if you had no understanding of what you were experiencing.
It is also known that when children's emotions are high their logic is low and vice versa. It has to do with the bridging of right and left brains which isn't complete enough to deal logically with emotions in the average child until five or six - even then they struggle.
You can teach your child, just as you can with reading, and help them understand their feelings, needs and emotions earlier. But you can't do this by ignoring their attempts to express them.
If a newborn baby cries we know it has a reason and we follow the list until we find out what it needs. But for some reason once a baby has a few words or can walk we expect them to suddenly have access to higher thinking without us ever teaching them how to have these higher thought processes or having time enough in the world to have learned.
The only answer to stopping the whinging is to find it's source - and to accept that sometimes your baby (and they are still babies) just desperately wants to reconnect with you no matter how inconvenient it may be for you.
So step one - help them label and understand their feelings and needs. It is best if this is done at times when they are not whinging and then followed up after the whinging is solved. Eg
you were upset because you wanted a biscuit. That feeling you had was hunger. You were hungry. Next time you can say biscuit or point to the biscuit and mummy can help you. Don't expect it to work immediately it takes some time for children to understand what they are feeling - especially since the same feeling can encompass many desires.
Step two - when they are emotional help them to regulate themselves so that they can access their logical thoughts and better express themselves. If a child has got themselves into a state you will need to distract them first and help them to regulate their emotional state - they cannot think clearly when they are emotional so you need to guide them through this process.
Step three - as hard as it is to get anything done - all too soon you'll be begging for hugs. Keep connected with your child and let them know that no matter what their feelings are you are interested and you want to help them. We are all entitled to feel the way we feel. It may not be something that mum or dad can neccessarily do anything about but they are nevertheless entitled to their feelings. Ackowledge the feeling, label the feeling, explain why they feel that way and then deal with it by fixing it and giving them the cookie or explaining that they can't have a cookie but they could have a banana if they're really hungry.
Step four - avoid putting adult thoughts into your child's mouth. They have not had enough time in the world or enough experience to think the way we do. Remember they are an empty slate that you are filling it in. So you can fill it in with
Mummy understands that you're angry and that's okay you can be angry sometimes, you still can't watch tv, but it's okay that you feel angry about this [/b](remember to provide an alternative to their desire if you are going to say no) - or you can fill it in with
stop being silly i've said no and that's the end of it now stop your whinging because I don't care and I don't want to hear it.[/b]
Have a think back through your childhood - remember emotional times how they were handled and how that made you feel better or worse. It may help you understand what your bub is going through.
Remember empathy is something we teach our children by exercising it ourselves.
Best of luck