Examples include:

• Mitochondria
• Chloroplast
• Peroxisome/Glyoxysome
• Endoplasmic Reticulum
• Nucleus
• Vacuole

Not all of these are found in the same type of cell. Most prokaryotes lack organelles (by definition, they lack a nucleus). Ignore alex.tan, he's a medic :P

As for what an organelle is I suspect that being membrane bound is the best definition. I disagree with Gritchka; the ribosome is a cellular machine, and was never an independant entity. I guess it's not too important anyway.

See: Endosymbiotic Hypothesis

Don't forget the following:

Golgi complex (a.k.a. Golgi apparatus) and lysosome (another way to say peroxisome).

By definition, prokaryotes do not have organelles but eukaryotic cells do.

By definition, prokaryotes do not have nuclei. Their genetic material floats freely in their cytoplasm. There is in principle no reason why they mightn't have other organelles.

They do, if we consider ribosomes to be organelles. What exactly is the definition? None of the above write-ups are precise enough, and I don't know the answer. A ribosome doesn't have a membrane, but it is a complex structure within the cell. I think that lets it count as an organelle.

However most of the organelles of a eukaryotic cell are believed to derive from earlier free-living prokaryotes that entered into symbiosis with a larger cell: this is the endosymbiont hypothesis of Lynn Margulis, and disposes of chloroplasts and mitochondria.

A membrane-bound body found in the cytoplasm of the cell that performs specific cellular functions.

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From the BioTech Dictionary at http://biotech.icmb.utexas.edu/. For further information see the BioTech homenode.