Kids perpetually want things, taking responsibility of what he/she already has, is a good bargaining point of ever being trusted with something else.
Remember that kids want to be trusted, and if they understand that looking after their pet is one way of maintaining your trust and respect, they will do it. Most parents don't want, or desire a pet from the start, but the little furry creatures never fail to warm your hearts. Just remember to start small, fish or little rodents are ideal.
A child soon learns (if the parents make it clear) that a living creature's life depends on their actions, they think that this is "cool" and react likewise. This seemingly tiny start at taking care of another creature, builds the infrastructure of caring for, and taking responsibility of bigger, more important things when they grow older.
Trust is a well-known esteem builder. This experience at a young age, cultivates in a child, the understanding of how we as humans react to positive attributes in others. Having experienced this respect of self, the child grows up to believe that he/she is able to work towards completing tasks.
This is our aim. The pet, and all its other advantages, is therefore serendipity. It is a means by which we teach our children that yes, despite what the masses believe, we are responsible to and for each other. This is by no means the only way to teach this lesson, but it is one of the most enjoyable and fulfilling ones I know.
The bottom line is that the parent understands that it's your job make the child aware of your role, and his/her role where the pet is concerned. You are responsible for buying the food, toys and straw (where applicable). He/she is the mummy/daddy, providing care, love, and time, and making sure that the pet is fed, watered and cleaned.
As kids don't remember new things that readily, all this could be written out on a board, or in the form of a contract. They will see it every day, so there is no ambiguity about what needs to be done. This in itself, is a step towards becoming responsible.
If a pet is totally out of the question, a high maintenance house plant will have to do.