What effects did slavery have on Europe?

These are good and thought-provoking answers.  Serfs often lived in conditions so bad as to make slavery seem a vast improvement.  Slaves could not be taxed, and so their taxes could not be collected in advance, sometimes several years in advance, which happened frequently to serfs in Western Europe from the 13th Century on.  Serfs, however, were "owned" by the land they lived on, not owned as personal property by individuals.  If the owner of a slave sold his manor house or lands or castle, he took his slave with him.  The serf remained on the land, no matter who owned it.

Slavery was much the same in Europe as everywhere else throughout history, only less prevalent than in earlier cultures because of the fuedal system of serfdom.   Where in the ancient world wars always led to mass enslavement, this was rarely the case in Europe past about AD 1000.  Vikings had raided for slaves for centuries, as had the Irish until the 5th Century, when St. Patrick converted the Irish and ended slavery there (probably the first nation on earth to extinguish the practice).  Patrick himself had been a slave, captured by Irish raiders when a teenager.

The case was a little different in Eastern Europe, where Germanic or Bohemian peoples warred and took slaves from the Slavic peoples.  "Slav", in fact, means slave.  Of course, the southern Slavic peoples were ruled for centuries by the Ottoman Turks, among whom slavery was widespread.  The people who were really made rich by the slave trade were Arabs.  Statistically, very few African slaves were brought to America.  Almost all were sold to Arab countries or in the Indian subcontinent.  Central and Eastern Africa was nearly denuded of people by the slave trade, but the vast majority of that happened in the 1870s through the 1890s.

The food supply of Europe is a whole different matter.  It was the limits of technology that led to periodic famines.  Agricultural techniques had achieved parity with the population of Europe by the beginning of the 14th Century.  The "Little Ice Age" of that time, resulting in short, cool summers, made famine inevitable.  The technology to ship foodstuffs long distances did not exist, either in preserving the food or in shipping.  In hard times, if one did not live in an unusually productive agricultural area or along a major river, starvation was a real possibility.  Between short summers, the limits of contemporary technology, war, bandity and two occurences of the "Black Death" the population of Europe in 1401 was about half what it had been in 1301.