The pieces that should concern you the most are the CPU cooler and the GPU.
A small CPU cooler like the stock Intel heatsink is of no concern. But if you have a big, 3lb, 140mm, dual tower monster then you risk putting too much strain on the motherboard when moving the computer around. If you have something like this then you need to look into ways of securing it, else be very very careful when moving.
The GPU can be a concern for the same reason, it's big and heavy and attached to the motherboard. If you have a large heavy GPU you can either remove it during travel or ensure that it is tightly screwed down to the I/O shield and moving it carefully.