Looking for patterns, trends and discrepancies—plants and algae are mostly autotrophic but some are not.
This is another NOS post that deals with the never-ending exceptions that arise whenever we seem to encounter a biological rule!
Back in Topic 5.3 (Classification) we learn that Kingdom Plantae is defined as containing organisms that are multicellular, photosynthetic and eukaryotic. Photosynthetic cells implies that the organism is autotrophic, but it turns out that this is not always the case!
The obvious exception would appear to be the carnivorous plants, such as the Venus Fly Trap (Dionaea muscipula) or the pitcher plant (such as Cephalotus sp.).
However, these plants retain their photosynthetic abilities and can even be raised successfully without providing any insects for them to eat (Rice). According to Rice (2007), this makes them only partially heterotrophic, as they still derive a large proportion of their energy from photosynthesis.
The true heterotrophic plants are those that are parasitic or saproptrophic. A great example of a parasitic plant is Rafflesia arnoldii, the plant that produces the largest flower in the world. It is a parasite of certain jungle vines and produces no roots, shoots or stem. In fact, it is only visible when it flowers. It gains all its nutrition through its parasitism of the host plant.
Similarly, there is a bewildering diversity amongst algae of organisms that are facultative and obligate heterotrophs. Many of these species have, like Rafflesia, become parasites, such as the genera Helicosporidium and Prototheca. Others, such as the fascinating genus Polytomella, have four flagella and are motile heterotrophs.

As always, biology refuses to be put into a box!
Sources:
Davis, Troy. “ Fully Open Flower of Rafflesia Arnoldii.” Rafflesia Arnoldii Robert Brown, Southern Illinois University, 29 Oct. 2010, parasiticplants.siu.edu/Rafflesiaceae/Raff.arn.page.html.
Figueroa-Martinez, F., Nedelcu, A. M., Smith, D. R. and Reyes-Prieto, A. (2015), When the lights go out: the evolutionary fate of free-living colorless green algae. New Phytol, 206: 972–982. doi:10.1111/nph.13279
“Polytomella.” Polytomella, EOL, http://www.eol.org/pages/90494/details.
Rice, Barry. “Are Carnivorous Plants Autotrophic or Heterotrophic?” The Carnivorous Plant FAQ: Autotrophic or Heterotrophic?, Jan. 2007, http://www.sarracenia.com/faq/faq1100.html.
“The Albany Pitcher Plant.” Cephalotus Follicularis – the Albany Pitcher Plant, Botanical Society of America, botany.org/Carnivorous_Plants/Cephalotus.php.
“Venus Fly Traps (Dionaea Muscipula).” The Mysterious Venus Flytrap, Botanical Society of America, botany.org/bsa/misc/carn.html.