Yes, in fact there are ribosomes in both plant and animal cells.

That is right. Ribosomes are the site of synthesis of polypeptide chains; proteins are formed from polypeptide chains. Both animals and plants need proteins for many purposes, not least as enzymes.

There are also ribosomes in prokaryotic cells, but these are smaller. The ribosomes in prokaryotes have a sedimentation rate of 70S (Svedberg units); eukaryotes have 80S ribosomes.

They are the sites of protein synthesis, which makes them as important as other cell organelles.