Because of the geographical location and language advantage, I have been shopping from Chinese websites (taobao, same vendors usually sell on ebay internationally) for years. Here are some experiences:
1. "Jellybean" parts are 90% fake. This includes voltage regulators, electrolytic caps, tantalum caps, MOSFETs, BJTs, Diodes, Opamps, FT232/PL23xx.
2. MLCCs are remarking of domestic brand. Take caution of large value and small package caps. I have encounter whole reel of 1uF 0603 cap shorts itself after extended burn-in test. Small values are OK.
3. Resistors are remarking of domestic brand. Tolerance could be over specified, but it is usually safe to use unless precision parts. 0.1% 6ppm SMD resistors (green color) are fake (value is ok, but drifting is bad).
4. ST MCUs are real. This includes STM8 and STM32 series due to ST's aggressive marketing.
5. Atmel are mostly refurbished parts, especially ATMega8/16/328/32U4. They usually comes in small volumes.
6. Low end Microchip are rebranded Haier chip. Middle and high range PICs are real.
7. Other brand MCUs are usually real. The technology has exceeded counterfeiter's capability.
8. Many LT, BB and AD parts are reused parts salvaged from old equipment. If the seller has labeled them as reused parts, they are often real. New LT parts, if too cheap (<$0.5), are blank or some other chips that happen to have the same marking as LT.
9. NAND Flash memories are reused parts. NOR flashes (MX25 type) are remarked domestic brand.
10. Parts having a Taiwanese compatible counterpart (such as nRF24L01) are the remarked Taiwanese parts.
11. In case of built-up modules, guess what they did to reduce cost.
Good luck