What are the differences between the processes of 3D printing with plastics versus metals? Why is metal such a problem? There are plenty of metals with low melting points. And AFAIK metal can be sprayed and directed in a number of ways such as with electric arcs and similar.
Metals are used. Albeit, in machines that are much more expensive and complex than your run of the mill FDM style machines that you're likely referring to.
The main reason you don't see many or any metal printers(SLS) and DMLS are likely due to patents and costs. They use lasers and special powdered materials with a binding material them. See Wikipedia links.
For instance, when the patent for FDM type plastic printers expired, the market flooded with lower cost machines and parts. When the patents for SLS expire, expect to see more of those type of machines hit the market.
That all said, there is a small team in Europe called Sinterit working on an affordable SLS machine. http://www.sinterit.com/ I'm not sure it can print metal. Again, maybe due to power requirements/patents/etc.
There may be others working on them too.
There are a number of practical processes for 3D printing in metals using various powder sintering techniques as described in other answers.
However it is difficult to use the sort of direct extrusion processes that you see with plastics because most metal alloys don't have the same sort of viscous, self adhesive phase that thermoplastics do. Most molten metals are fairly fluid, cast iron, steel, bronze and aluminium have a viscosity not too far off water when melted if there is an intermediate phase it is usually a slush mixture of solid and liquid phases rather than something which can be extruded and adheres to itself.
There is also the consideration that consumer 3D printing is designed for relatively inexpensive low volume production, so trying to do the same thing with metal is likely to be self defeating. In most cases it is likely to be easier to print a pattern in wax and plastic and investment cast it if you want it in metal.
Similarly in the case of low melting point alloys it is just as cheap and almost easy to make a silicone mould from a master and cast it plus the fact that modern resins may actually be superior to low melt metals in most respects.
One example of this is is the models used for table top games. A decade ago these were injection moulded plastic for simple models and white metal for more detailed ones. Now they are almost exclusively cast resin.
There is also the fact that metals are inherently a bit more versatile than plastics in terms of rapid prototyping and fabrication. So there are more competing options for low volume manufacturing of metal parts than plastic ones.
In terms of direct equivalents to plastic filament extrusion in metal MIG welding is not that far off inn terms of process and a robotic version of the process is certainly reasonably plausible, however as already discussed the flow characteristics of metal mean that MIG certainly doesn't have anything like the resolution of plastic extrusion as there is a minimum voltage/current which is required to strike and arc.
There is also the fact that a decent MIG welder which produces anything like a consistent weld bead would start at around £500 with the 3 axis control on top of that, plus the fact that MIG generates a lot of fumes, spatter and UV radiation which needs to be managed.
TIG welding offers a bit more precision but is equivalently more expensive for the basic machinery and an automated setup would require additional wire feed equipment.