As it turns out, reality is much more complex than either theory allows for. For the most part Mendelian inheritance is the rule. Some traits are the result of multiple genes, so they don't appear to display Mendelian inheritance, but with the advent of genetics we now know that they do. However, there are cases of soft inheritance to be found (e.g. epigenetics  and prions ).
I have come to the conclusion that stupidity in human beings is inherited through both Lamarckian and Mendelian mechanisms. Allow me to explain. Not long after Lillian was born , I saw a woman in her twenties pulling a baby stroller up the stairs next to the Botany Pond on BYU Campus in Provo, Utah. She was facing forward and was dragging the stroller—ka-chunk! ka-chunk! ka-chunk!—rapidly up the stairs behind her, with no regard for how hard this was jolting the baby inside (which looked to be under 6 months old). This woman was in possession of some genes that inclined her to do something stupid. And she more than likely passed some of them on to her child in the stroller. That's Mendelian inheritance. But her stupid actions also jostled the brains of her infant, making the child more stupid, too—and this independently of any shared genes. That's Lamarckian inheritance.
There's more to it than that, though. Intelligent parents are more likely to introduce reading to their children at a younger age, thus helping them to increase their intelligence (Lamarckian inheritance) in addition to the genetic component of their intelligence (Mendelian inheritance). Conversely, less intelligent parents are more likely to wait to teach their children to read—or will perhaps even put it off all the way until the child enters the public education system. This is just one example, though I'm sure there are more.
 This is also sometimes called Lysenkoism (though Lysenko himself called it Michurinism).
 See http://en.wikipedia.org/wiki/August Weismann#Experiments on rats.
 Epigenetics refers to inherited traits which are not the result of genes being transmitted from parent to offspring. One example of this is the lipid membrane that surrounds all cells. When a cell divides half of its membrane goes to each daughter cell. Thus lipid membranes are inherited independently of DNA and obey the rules of Lamarckian inheritance. For more information see http://en.wikipedia.org/wiki/Epigenetics.
 Prions are misfolded proteins found in the brains of mammals. They aggregate outside of brain cells, eventually leading to huge masses, called amyloids, which disrupt brain tissue. Some of the more well-known diseases caused by prions include bovine spongiform encephalopathy ("mad cow disease"), scrapie of sheep, chronic wasting disease of deer and elk, Creutzfeldt–Jakob disease (CJD), and kuru. When a misfolded prion encounters a correctly folded protein of the same variety, it causes that protein to also misfold. Since no genes are involved and an acquired physical trait is conferred to "offspring", this can also be considered Lamarckian inheritance.
 See my post Unexpected Delivery.
 See a panoramic photo of the Botany Pond here (scroll down).
Giraffes is by Clémence Delmas, available at http://commons.wikimedia.org/wiki/File:Girafeskoure.jpg.
Punnett Square is by Madprime, available at http://commons.wikimedia.org/wiki/File:Punnett square mendel flowers.svg.