Is abiogenesis possible today?
I will argue that yes, it is POSSIBLE. It is possible on earth like on other planets. Given enough time, matter, and energy, "something" that resembles life will emerge. The problem I see, however, is that life has already conquered our planet, so any "new living thing" will have to compete with other long-time adapted living thing, in practice, no chance of survival. The right conditions you refer to are the ones that allowed "life as we know it" to emerge. Given other conditions (other chemicals, other energy forms, etc), something completely different will form.

Of course, without final proves, this is still speculation.

Some speculative links:

http://speculativeevolution.wikia.com/wiki/Alternative_biochemistry

http://www.dailygalaxy.com/my_weblog/2015/05/alien-life-habitats-nasa-brainstorms-alternatives-to-water.html

http://www.nature.com/news/2009/090513/full/news.2009.471.html