This particular question has been of a great deal of interest to me, especially since it dives at the heart of abiogenesis.
In 2010, Dr. Craig Venter actually used a bacterial shell and wrote DNA for it.
Scientists have created the world's first synthetic life form in a landmark experiment that paves the way for designer organisms that are built rather than evolved.
The new organism is based on an existing bacterium that causes mastitis in goats, but at its core is an entirely synthetic genome that was constructed from chemicals in the laboratory.
Keep in mind, this is only a synthetic genome, not a truly unique organism created from scratch. Although I am confident that the technology will become available in the future. As has been pointed out, the entire genome wasn't built de novo, but rather most of it was copied from a baseline which was built up from the base chemicals with no biological processes, and then the watermarks were added (still damn impressive since they took inorganic matter and made a living cell function with it). But they are working at building a totally unique genome from scratch (PDF).
This is actually quite an emerging field, so much so that the MIT press has set up an entire series of journalsfor this. As far as to the purpose of these artificial organisms, most research funded by companies are meant to be for specific purposes that biology hasn't solved yet (such as a bacteria that eats a toxic waste or something). Although, a lot of people are concerned about scientists venturing into the domain of theology.
In terms of abiogenesis, there are many resources to learn more about this. Here is a list of 88 papers that discuss the natural mechanisms of abiogenesis (this list is a little old, so I am sure that there are many, many more papers at this time).
I also found this list of links and resources for artificial life. I cannot verify the usefulness of this since the field is a bit outside my area of expertise. However, it does seem quite extensive.
EDIT TO ADD: Now we have "XNA" (a totally synthetic genome) on the way.
In principle it is possible. Life doesn’t contain some divine or intrinsically spiritual element that we would have to add to our artificial organism potion to breathe life into it. At this moment we are limited by gaps in our knowledge and by the current state of technology.
We first have to better understand fundamental principles of life on a multi-level scale: from quantum mechanics, through biochemistry, structural biology, molecular evolution, to macroscopic function and behavior on the organism level. This, together with development of enabling technologies, will require decades of research but some steps have already been taken.
One of the promising approaches is re-writing, as exemplified in this work:
We redesign the genome of a natural biological system, bacteriophage T7, in order to specify an engineered surrogate that, if viable, would be easier to study and extend. (...) The resulting chimeric genome encodes a viable bacteriophage that appears to maintain key features of the original while being simpler to model and easier to manipulate. The viability of our initial design suggests that the genomes encoding natural biological systems can be systematically redesigned and built anew in service of scientific understanding or human intention.
or a minimal cell synthesis project:
Construction of a chemical system capable of replication and evolution, fed only by small molecule nutrients, is now conceivable. This could be achieved by stepwise integration of decades of work on the reconstitution of DNA, RNA and protein syntheses from pure components. (...) Completion would yield a functionally and structurally understood self-replicating biosystem. (...) Our proposed minimal genome is 113 kbp long and contains 151 genes. We detail building blocks already in place and major hurdles to overcome for completion.
So, technically it’s very difficult but definitely can be done, which is really exciting.
I would like to add a lecture on Synthetic Biology by Andrew Hessel, who introduces the open source synthetic biology field, compares it to computing, and gives an overview of what are its applications, like the creation of the first synthetic organism.