In my opinion it highly depends on your assembler.
As Daniel Giesbrecht mentioned - most of the SMD components nowadays come in a "pick and place friendly" packaging. That is - they will be supplied in tape, with plastic caps or masking kapton stickers so the machine can pick it up. But unfortunately it comes with a price - literally. Most of the time parts in tape will be more expensive (sometimes very significantly) than parts in bulk (in trays, bags etc.).
Second problem is the assembler - or, to be exact, it's capabilities. Yes, you can buy, for example, a 80 pin SMT connector in tape. But this tape will be very wide (72mm or even more). To feed this tape into the pick and place machine you need a feeder that is 72mm wide. And not many assemblers will have that kind of feeder because it is very expensive and rarely needed. So when you go to a smaller assembler, they will either order the same part in tubes/tape - and place it manually, or cut the tape to strips and stick it (sometimes literally) inside the machine and use it as a tray of components.
There are also problems with the height of the tape, weight of the parts and nozzles used to pick up the part.
When it comes to components that will be placed (probably) without a problem - all of the standard "chip" components, IC's, tantalums, electrolitics, inductors, basic connectors. All of them in tapes ranging from 8mm to around 32-44mm (to be on a safe side).
In summary - what you consider a "component placed by hand" is highly dependent on your contract assembler. If you have any "non standard" parts - like very large IC's, large connectors, mechanical parts (studs, spacers, terminals), switches, heavy parts, large electrolytic capacitors etc. - contact your assembler and ask if they will be able to place them automatically.