As an off-shoot of the Asian Buddhism thread, here we can discuss any challenges to Buddhism in the modern world and here Buddhism can mean in the "West" or in Asia.
“Wander forth, O bhikkhus, for the welfare of the multitude, for the happiness of the multitude, out of compassion for the world, for the good, welfare, and happiness of devas and humans. Let not two go the same way. Teach, O bhikkhus, the Dhamma that is good in the beginning, good in the middle, good in the end, with the right meaning and phrasing.” Samyutta Nikaya 4.453
In the modern world there seems to be two schools of thought: some who say let people come to the Dhamma on their own, when the time is right and another camp that would like to help others come to the Path of the Dhamma in ways that might be seen as missionary. I am of the latter and feel that this can be done in the spirit of the teachings, in a gentle and compassionate way. For example, offering 'Introduction to Buddhist meditation' workshops at Dhamma centers and temples and placing fliers and advertising such events.
Hedonism seems to be the religion of the modern world and there is not much Buddhism can offer those who are attracted to hedonism. But another 'religion' of the modern world is science and scientific method. In my opinion, this is an area where Buddhism can really shine and attract those inclined to science. Buddhism is at least compatible to the sciences and scientific method (in at least the use of empiricism, observation, and analysis). Astronomy, biological evolution, and others are at least compatible with the teachings of Buddhism.
The arts are another area that remains popular from ancient times through modern times. The Mahayana has probably had better luck with the use of the arts as a Skilful means for expressing the Dhamma and perhaps this is an area where Buddhism or Buddhists could focus some efforts on.
Well, this is an opening post, but it looks more like some possible 'solutions.' Feel free to offer more possible solutions, thoughts, or challenges Buddhism faces in modern times.