Here's what we have so far. Note that these are not necessarily "good hearted" reasons, and some of these obviously do not apply to many people.
Purely altruistic reasons ("want to bring a life into the world") etc
Spread your genes/win at natural selection
Want to experience parenthood
Religious requirement e.g. "go forth and multiply"
Refusal to use contraception
Don't know/understand how to use contraception
Work on the family farm, help out around the house, etc
Kids earn money which they repay back to their parents (in many cultures)
Hope that your kids become successful/rich and in turn help you out (e.g. your children become successful businesspeople, doctors, engineers, etc)
Try to "Lock down" a suitable partner
Many people believe more people is better for the world, or that they will do a good job raising their children (to be doctors, scientists, inventors, etc) and are good for the world in that way
Political fecundism (defined by Wikipedia as "to increase the numbers of a group and, consequently, its political influence)
Other demographic reasons (e.g. try to increase the number of your religion, your ethnicity, your political beliefs, etc. For example, if you are a diehard supporter of gun rights, or gay rights, communism, capitalism, etc, having a large family who you try to raise with these beliefs, increases the demographics of your cause)
"Marriage alliances". Think Game of Thrones, but a more modern version. In other words, hope that you have successful kids who themselves marry successful, wealthy people, etc. Having politicians, doctors, engineers, rich businessmen, etc, as your son/daughter in law, or son/daughter in law's parents, can give you a huge amount of contacts, influence, family favors, etc.
Continue family name
Protection (e.g. live in a rough neighbourhood, having 6 big tough sons is probably a good deterrent)
Look after you when you're old and can't work (in poorer countries with no social security this is huge, also varies a lot with culture)
Claim child welfare and other benefits (I personally know quite a few people who make a "profit" from child benefit, here in the UK)
Tax relief
Political/image reasons, e.g. a politician/boss who wants to be seen as a "family man".
Can you think of any more?