Flowering Structures
All conventional palm species begin producing flower clusters once they reach sexual maturity (as fast as 2 years with some Chamaedorea sp. and as slow as 40-60 years with Tahina spectabilis).  Some palms are monoecious (having both male and female flowers on the same tree), while the rest of them are diecious (having male flowers on one tree and female flowers on a different tree).  Some monoecious palms that have been hybridized are Wodyetia, Butia, Jubaea, Hyophorbe, Syagrus, and Sabal.  Some diecious palms that have been hybridized are Chamaedorea, Rhapis, and Phoenix.

A palm seed forms once a pistillate flower (female) receives a grain of pollen from a staminate flower (male).  The period in which the male flowers open and expose their pollen and the female flowers open to receive their pollen is called anthesis.  Monoecious palms (Right picture) each produce both male and female flowers on the same tree and are more difficult to hybridize because you have to emasculate the inflorescence (remove all male flowers) so that the palm cannot create seed by itself.    Then, male donor pollen from another palm has to be applied to the female flowers in order for them to become “pregnant” and become a seed (which will grow into a new palm tree).  Diecious palms are easier to hybridize because all you have to do is remove the inflorescence from a male tree and shake the pollen off onto the inflorescence on a female tree to create hybrid seeds.
F1 and F2 Hybrids
If a palm tree is cross-pollinated by hand (Right Picture) and the resulting hybrid seed is sprouted and grown into a tree, this tree is known as a F1 hybrid.  If this F1 hybrid grows and reaches sexual maturity, it will produce its own seed (if it is monoecious; see above).  If this seed is successfully sprouted and grown, the resulting tree is known as an F2 hybrid.  Essentially, an F2 palm hybrid is one that was grown from seed collected off an existing hybrid.
A hybrid palm (such as a Mule palm, or xButiagrus), can receive pollen from a donor that is flowering in close proximity.  This creates a back-cross.  For example, a Mule palm is a Butia x Syagrus (Jelly Palm crossed with a Queen Palm).  If this mule palm produces a flower cluster (inflorescence), it generally cannot pollinate itself (even though it has both sexes of flowers).  Thus, if a bee carries pollen from a nearby Queen Palm (Syagrus) and drops it on a female (pistillate) flower on the Mule Palm’s inflorescence, the female flower may grow into a seed.  If this seed is sprouted and grown, the resulting tree would be a Butia x Syagrus x Syagrus.  This new back-cross should closely resemble a Queen Palm, but still have slight characteristics that resemble a Jelly Palm.  Conversely, the Mule Palm (Butia x Syagrus) can donate pollen to a third genus such as the Chilean Wine Palm (Jubaea chilensis) to create a Jubaea x (Butia x Syagrus), or a Jubutigrus.
(Left picture) A suspected Butia capitata x Cocos nucifera.  If this hybrid is confirmed, it will be the first time in history the Coconut Palm has been crossed with another genus (Butia).  This could result in a million-dollar cash crop if somebone was to produce it commercially!
As long as a group of palm species are in the same family, they typically contain a similar number of chromosomes within their genome and thus can be hybridized with one another.  Butia, Syagrus, and Jubaea are all in the same cocosoid family.  Cocos, Parajubaea, Allagoptera, Lytocaryum, and Jubaeopsis are also in the cocosoid family and can be hybridized with each other.