How far is stem cell research from being to generate a new organ?
Sperm can already be generated using stem cells http://blogs.discovermagazine.com/d-brief/2016/02/25/scientists-grow-working-sperm-from-stem-cells/#.V-UADBV94o8
Also, heart, liver and kidney cells as well.
http://www.popsci.com/scientists-grow-transplantable-hearts-with-stem-cells
http://www.ncbi.nlm.nih.gov/pubmed/26458176

Full organs are still far. The main problems are to grow them separately from the rest of the body (embryonic development) and to vascularize them.
One solution is to grow them in other animals http://www.dailymail.co.uk/sciencetech/article-3442818/Growing-human-organs-farm-creatures-takes-step-closer-New-guidelines-allow-research-human-animal-hybrids.html

There are experiments done with some success in using "decellularized" kidneys as a scaffold to "grow" a new kidney by perfusing stem cells into it. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4927010/

There are the so-called organoids, very little agglomerates of different organ-specific cells differentiated from stem cells. They are far from being functional organs but it's definitely a start. http://hub4organoids.eu/organoid-technology/

Some labs are experimenting with 3D printing. They use stem cells to derive all the organ-specific cells needed and then they try to rebuild a functional organ by printing cell by cell, layer after layer. http://www.nature.com/nbt/journal/v32/n8/full/nbt.2958.html

Lastly, embryonic stem cells are not strictly needed anymore, they can be substituted (in most of the cases) by iPS that can be derived from many different adult cells (i.e. no embryo is needed).