Americans Abroad

Things we wished we had taken -
Books (especially cookbooks and art books)
Music CD's - and yes, they are still a thing here.
More of our DVD's - we have a Sony player that runs on 12 volts that we brought with us.
Photographs and some other memories.
Some art.
My Le Creuset pots and my mother's cast iron frying pan.

Things we are glad we left behind:
Any appliances
Stereo equipment - if mine had been dual voltage I would have found a way.
Furniture - though I do miss the dining room table, even though it wouldn't have fit in our present flat.

Things not to bring:
Beds and mattresses because you will not find linen to fit. You will pay a lot for mattresses in France (can't speak for the rest of Europe), and be aware that the beds are smaller. It is possible to get larger ones, but rooms are smaller, so be aware of that.
Kitchen appliances - despite what people say about getting converters, it's just not worth it.
Hair dryers, curling irons, and any other electrical devices unless they are marked to run 110-240V 50-60Hz - if they are you only have to get plug adapters.
Lamps (unless you want to get them rewired).
Furniture - mostly you'll find what you need.

We've known some people to bring cars over, but that's a whole different thing. Probably helps if you've got lots of money. Be aware that the market for used cars is large and generally not what you would expect in the US. People generally take better care of their vehicles and so the resale value stays high. There is also a tendency to hold onto vehicles longer here. We paid just over 6000€ for a 2009 Renault Modus with 137,500kms on it.

We didn't ship stuff over. We brought over multiple suitcases on multiple trips. A container might have been cheaper, but that's hindsight. We even brought over my vintage Martin guitar as hold baggage. Bought a hard case from Gator Cases and the guitar arrived without a scratch. And that was with two luggage transfers - Philadelphia to Boston, Boston to Lisbon, Lisbon to Marseille.

We put some stuff in storage, and then a year later had a friend go and clear it, sort it, and send a suitcase over with the selection. Unless you're intending to go back, storage is just another expense that you'll regret.

When we actually decided to make the full jump, we had 45 days to clear out our 3 story 2000sq ft house with basement. Some stuff we moved too quickly with and hence there were some regrets. And you'll find that you unpack something and look at and go 'What were we thinking?' and laugh.

Just saw your thing about baking powder - here in France it's levure chemique in the pink packet with the Alsace lady on the outside.
Hope this helps.

Oh yes - because I cook, I brought all my knives apart from a bread knife or two. And I've still bought more here.