What PCB components typically require hand assembly or are associated with difficult assembly?
Some features I've seen on parts that require hand assembly:
Unbalanced part. If the center of gravity of the part isn't over the parts of it that contact the board, it will fall over before it can be soldered down, unless specially handled.
Low-temperature part. If the body of the part is made of (some types of) plastic, or contains some low-melting point metal, it may not be able to withstand the heat of an automated soldering process. And it will often also have a spec about the maximum time to keep the iron in contact with it during hand soldering.
Mixed mode assembly. If through-hole and SMT parts are mixed, it may be more cost effective, in a small production run, to hand-solder the through-hole parts.
Most surface-mount components are designed to be machine-placed. A Pick-and-Place machine uses a system of cameras to precisely place components, via suction.
Some components are difficult or impossible to pick up with suction. In those cases, it is common to see something like this:
The flat plastic cap provides a surface area for the machine to pick up the part. After assembly, the cap can be slid off.
Generally, through-hole parts require hand placement, or specialized equipment. Sticking with surface-mount parts will make it a lot easier for manufacturing.
Also, as was mentioned in the comments; if the part comes in a reel, that's a pretty safe bet that it can be machine-placed.
When in doubt, ask your board assembler for details about their capabilities. They may be able to help recommend alternatives to hand-placed parts.
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).
TL;DR 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.