Bulbs
Various techniques involving division of the actual bulb, may be used to propagate some of the species that grow from them, i.e. lilies, Alliums, Fritillaria, Hyacinthus, and others.
The following three techniques cannot be used interchangeably: if in doubt whether a technique may be used, then consult the species databases for more information. Also, do not commit all of your bulb material to one of these procedures, since success is never certain. In particular, fungus can easily ruin the experiment.

Bulb Scaling
Plants of the genus Lilium as well as some others, grow from bulbs consisting of overlapping scales arising from the basal plate. These bulbs may be lifted in early fall, and individual scales may be snapped off carefully, holding the scales as close to the basal plate as possible; if scales are limp, a sharp, clean, sterilized knife may be used. A small section of basal plate should come off with the scale; new growth will originate at this point. Remove as many scales as are needed, with a few extras for good measure, then replant the parent bulb. The whole bulb may be 'scaled' if required.
Dust lightly with anti-fungal powder, and mix scales into lightly dampened vermiculite; store warm, dark and slightly moist for 2-3 months, then move into the refrigerator for 6 weeks. As bulblets form, pot them up with scales still attached, just covering the tops of the scales. Grow on in a protected location until a reasonable size, then move into their final locations, in spring.
Bulb Chipping
Again in early fall, lift dormant bulbs and cut them into quarters, or, for larger bulbs, into 8 or 16 pieces or chips, each with a piece of basal plate still attached. Use a clean, sterilized knife, and dust the cut surfaces with fungicide prior to treating the chips as one would bulb scales, above.
Twin Scaling
Twin scaling is similar to, though more traumatic than the two previous procedures. Bulbs are again cut into quarters, then each quarter is separated into pairs of scales, or twin scales that are still attached by a small part of the basal plate. Dust with fungicidal powder, and treat as above.