Besides the somewhat inconsistent customs regulations around the world regarding liquids in a carry-on bag, they can be a messy problem should they leak. So avoid packing any liquid products at all.
No, that doesn't mean you have to go without shampoo for your trip. You actually have several options. The easiest would be to just buy a small bottle of shampoo (or whatever other products you need) at your destination. This is fine for some places, but some exotic travel locations might not have the kinds of products you are looking for.
Another alternative is to pack solids instead. Boutique body product stores such as LUSH have several shampoo bars available, and can certainly make your packing easier. No spills and no airport fuss.
Same goes for toothpaste (usually classed as a gel, and may have airline restrictions). You can buy toothpaste powder instead.
