Free-standing: offer maximum flexibility as they are not permanently installed. Be mindful of weight restrictions and ensure they are assembled correctly for safety. Typically a short term solution for the laundry.
In-built: will be attached to the walls or floor in the laundry, can be open or with doors or a mixture of both.
Under-bench: if you have room for a laundry bench, you have a great space to add cabinets underneath it. Also known as base cabinets. Pull out base are very popular, but there is a market for doored versions or open cabinets for easy access to supplies.
Overhead cabinets: offer ideal storage and can more safely store cleaning chemicals. Can be installed above sinks, benches, washing machines and dryers. Overheads tend to last longer as they are not subjected to the same amount of wear and tear (like water) as under-bench options
Specialty cabinets: includes laundry chutes, detergent pull outs, ironing board cabinets, drying cabinets and for those with an upstairs, a dedicated dumbwaiter.
Of these cabinets, you may opt to have them custom built or buy pre-assembled, modular or flat-pack in standards sizes. Bespoke options will demand a higher price point, but are worthwhile to maximise the storage and utility of a laundry.