Are steam-powered trains still in use anywhere?

 Over 1400 steam locomotives around the world are still operational today. The UK has among the most extensive network of steam train services in the world. Reflecting the country's historic railway innovations, the UK has over 170 operational railways, running trains over nearly 900 km of track and operating between around 460 stations.

Most of these have steam trains in partial or total service. In North Wales, there is a 60 km narrow gauge network which exclusively operates steam trains. In North Yorkshire, there is a seasonal daily steam hauled train service operating for a 90 minute journey between Pickering and Whitby.

There are also plenty of examples in mainland Europe, North America, India and Australia. Germany has a number of narrow gauge lines with more or less regular operation and at least partial steam traction. Switzerland has the Brienz-Rothorn-Bahn, a cogwheel mountain line with partial steam operation. Austria has some steam hauled mountain lines, including the Achenseebahn and Schafbergbahn. Poland keeps steam locomotives operational at Wolsztyn, and a narrow gauge railway in Koszalin still operates as public transport using a steam engine. India uses steam locomotives on the Darjeeling and Nilgiri lines.

In the United States, the Union Pacific Railroad has its own steam locomotives used for public relations and advertising, and they boast that they have never stopped running steam. There are also tourist railroads such as the Durango and Silverton, which run purely steam-powered excursions. There is one place where steam is still occasionally used to haul revenue freight: the Strasburg Rail Road in Pennsylvania, which is primarily a tourist railroad but also an active short line that deals with local freight.

China was using steam locomotives well into the 2000s in the coal industry, but those have mostly been retired. The last commercially used steam trains were at Sandaoling, and they became a magnet for steam train enthusiasts worldwide.

Why did steam locomotives not have condensers to recycle the spent steam? The thermal efficiency would be a lot higher.

 There have been condenser locomotives, and they indeed do have double the thermal efficiency than the ordinary double acting steam locomotives. They have one major drawback: the condenser required is HUGE. The condenser really doesn't matter on ships or stationary power plants, but trains have these things called "payload" and "load gauge."

Hauling the condenser is about the same as hauling one extra fully laden freight wagon, and the condenser needs to be designed to fit within the load gauge. Moreover, on ordinary steam engines, the spent steam is fed into the exhaust to improve firebox draught, but condenser locomotives need an extra turbine to do so. Condensers could be heavy as well, which reduced the payload able to be hauled.

Condensing the steam meant the added complexity, and maintenance, of the fan needed to feed the blast pipe that pulled air through the firebox. Unless there was a compelling reason, it was easier to take on water at a station stop rather than add the complexity of condensers. Diesels replaced steam primarily because they required far less maintenance and they offered the flexibility of allowing multiple locomotives to be controlled by the one driving crew. The diesel electric locomotive had about 10 times the efficiency of the regular steam engine, and the condensing system couldn't compare even if it doubled the steam engine's efficiency.

Nevertheless, condenser locomotives have been used, and they have proven worth the extra investment in regions where distances are long, where water is sparse, and where fuel is expensive. Another extra benefit is that they do not leave the telltale vapour clouds behind them. The South Africans built 90 of these condensing locomotives from 1953 to work arid regions like the Great Karoo. Steam would be recycled up to eight times, giving the locos a 500 mile range. They had effectively sevenfold the range of ordinary steam locomotives, with no need to stop to replenish fuel and water. Deutsche Reichsbahn also used condenser tenders in Russia during the WWII, where distances are long.

Are nuclear power plants just a sort of steam engine?

 Essentially, yes.

The nuclear fission produces enormous amounts of heat and you use the heat to produce steam to drive a steam turbine which in turn drives the alternator.

It’s basically a conventional coal powered plant on steroids. A conventional coal powered plant uses coal to heat the water instead of nuclear fission.

Apart from photovoltaics, electricity is generated by driving the alternator ( electric generator) using a mechanical device such as a steam turbine, hydraulic turbine, gas turbines, diesel engines or IC engines or just about any device that will output mechanical energy.

A steam turbine converts thermal energy from high pressure and high temperature steam into mechanical energy which is outputted at the shaft of the turbine which in turn drives an alternator ( short for alternating current generator ) that produces electricity.

Similarly a hydraulic turbine converts hydraulic energy into mechanical energy that drives the alternator.

The difference between a coal powered plant and nuclear plant is how the water is heated and made into steam to drive the steam turbine. A nuclear plant uses nuclear fission which can generate enormous heat and that is used to generate the steam that drives the steam turbine. The only difference is the source of the heat for the steam.

And for people commenting that Beta Voltaics, Magneto Hydrodynamics, Fuel cells, batteries etc can produce electricity without a mechanical prime mover with the exception of photovoltaics, can any of them power an electric grid or produce enough power to do so? This specific answer pertains to power generation for an electric grid and other than photovoltaics, most others are incompabale of generating power to supply a grid and batteries are for low power devices ( cars with Li-Ion or NiMH batteries have to recharge through the electric grid mostly powered by conventional electric power generation and some from photovoltaics.