Are there still any trains from Kiev to Crimea?

Although no trains go directly to Crimea, it is possible to get very close to the de facto "border" by train and then traverse the remaining distance by bus.

One such option is to take a train to Novoalekseyevka from Kiev, then take a shuttle bus or taxi to the de facto "border" (checkpoint Chongar). Upon crossing the "border" and traversing the buffer zone on foot or by bus, you will be able to take another bus or taxi to all major Crimean locations.

Another option is taking a train from Kiev to Vadim by way of Kherson, but you will also have to take another shuttle bus to the "border" or walk on foot for 2 hours.

This page gives a breakdown of all possible options of getting to Crimea from other Ukrainian regions.

Please note that the above information was provided only for reference purposes to clarify the train situation. Crossing the border this way has plenty of drawbacks as well, such as having to procure a special permit from the Ukrainian government, falling prey to dishonest drivers and militia or raising suspicion at the Crimean border. Unfortunately, I'm unaware of a tourist-friendly way of getting to the Crimean peninsula as of 2018 that would leave both countries claiming its ownership happy.