What is my crude yield?

The crude yeild is the percent yield of crude product, i.e. that product initially isolated from the reaction mixture, prior to a purification step.

Should I report the crude yield in my notebook and in my experiment report?

Yes, whenever possible.  The crude yield gives an indication of how well the reaction went and provides an indication of how much material one can expect after purification (or conversely, gives information about material loss during purification).  It is most informative if one can obtain some analysis of the crude product (say by NMR) to determine its composition, but this will not always be possible.  If the crude yield is near 100%, then the reaction probably goes in high yield and one can expect a high final yield of purified product (assuming an efficient purification step is used).  If the crude yield is much greater than 100%, then one must suspect it is not reliable and there may be major contamination of the product by solvent or some reaction byproduct.  If the crude yield is low (say < 30%), then the reaction probably goes in low yield or a problem with isolation of the crude product has resulted in low mass recovery.

Is purification of crude product always necessary?

Usually, but not always. If the initially recovered product from the reaction mixture can be shown to be pure (by mp or NMR or TLC analysis), then further purification may not be required.  But often, the first isolated (crude) product requires a purification step to give pure material.

What are some common purification methods?

recrystallization (of solids)
distillation (of liquids), simple or fractional
chromatography (of liquids or solids)
sublimation (of solids)
extraction (of solids or liquids)

Is the reported yeild the yield after purification?

Yes, reported yields are assumed to refer to pure product.  Some indication of product purity should accompany the final yield report, such as bp range, mp range, TLC behavior, NMR analysis, GC/MS, etc.