Many people promote various different answers to this question. However, the main reason for this seems to be in order to manipulate the behaviour of others. This advice is obviously of low value for those trying to decide what to do.
Of course the bottom line is that most people are free enough to propagate whatever they like. So: please consider the rest of this article as my two cents:
From a scientific perspective there are three main classes of copied entity that have the most direct influence over human behaviour: DNA genes, social learning (memes), and individual learning.
The DNA genes with the most influence are usually those of the host involved, but sometimes the genes of other people, mutualists or parasites are also significant.
Human genes have delegated most of our behavioural repertoire to the human brain. So, in practice the brain makes most of the body's decisions that are more complex than reflex actions. However, genes still get to have their say - they originally designed the brain's reward system - constraining the brain's options.
In practice most humans act as though they are propagators of both genes and memes. The significance of gene-propagation is quite high - just looking at the seven billion humans. Indeed some opponents of memetics argue that the influence of genes is overwhelming - and that the common examples of deleterious memes (such as smoking memes and obesity memes) generally exist because they benefit the genes of various corporation owners). However, I think any sensible analysis denies the validity of the "it all boils down to genes" perspective - i.e. memetics beats Wilson-style sociobiology.
Some have suggested that meme propagation is personally important to them. Famous examples include Dawkins - who wrote:
I'd rather spread memes than genes anyway.
...and Steven Pinker - who wrote, in How the Mind Works:
I am happy to be voluntarily childless, ignoring the solemn imperative to spread my genes. And if my genes don't like it, they can go jump in the lake.
Personally I am much more sceptical about meme propagation at the expense of their gene propagation. I tend to regard it as memetic hijacking. I tend to view those who propagate memes at the expense of their genes as memetic hijacking victims. If memes steal your genetic genetic fitness, you are probably being manipulated.
Many seem to regard nature as "wasteful, cruel and low". They see gene propagation as bad. However, my perspective is rather the reverse of this: evolution is good.
Some regard personal gene-propagation as selfish - and advocate propagating their group, species or ecosystem instead. For example, The Laughing Genes recommends propagating high-level entities - such as your own species. I regard this advice as probably a form of signalling. Selfishness has a poor reputation, and consequently, many want to signal unselfishness. This appears to be the basis of much moral preaching promoting unselfishness.
What about the idea that memes are on the rise? That there is likely to be a memetic takeover - and so attempts to spread genes are ultimately likely to be futile?
It is true that in the last genetic takeover, few organisms from before the transition made it through. However, that seems unlikely to happen again. These days there are too many museums for anything to get that lost. Genes can still reasonably dream of immortality.
- Tyler, Tim (2006) Nietzscheanism