What technique could I use to re-color the doors, moulding, and cabinetry in my house?
You can go as dark as you want but once you go black, there is no going back.  There are a ton of stains on the market that specialize in staining over an existing stain.  You would have to test them out to find one you like in a recluse area of the house.  

Is the job a big deal?  For sure.  You may not think your trim and floors are modern looking or trendy, but just from the few pictures they are certainly done really nice.  And that is a really big deal.  You have some really clean lines and the staining is very uniform.  I would assume that if restained that it will not look as professional.  

Is it worth it?  If you truly aren't happy with it and you will be in the house a while then do it.  Are you expecting to gain equity because the house is more fashionable?   I could only see this working out if the house is very high end.  The fact is the current colors don't look bad at all and could be more fashionable in 5 years - and these colors are never out of fashion.

To do this right is just a ton of work.  Restaining is a bit easier on flat surfaces that are easier to control.  All the trim is curved with details.  Meaning it is going to take a lot more time and it will take a good deal of skill or trial/error to get it to look as good as it does now in a uniform darker color.