A short list of fake ICs I know exist:
PL2303 - Prolific doesn't sell those chips to retail distributors so rest assured all are fakes. Multiple different clone dies exist. IME they work OK, though
DS18B20 - I have seen two different clones, both don't meet accuracy specs, one is really bad even at room temperature. Beware of preassembled cables with those inside - you have no idea if they are genuine.
TL072 - multiple people reported fakes by now, it seems some kind of LM358 is inside because cheaper than JFET opamps.
NE5532 - you either get recycled chips of random vendors with NXP markings (NXP never made those chips, Philips did) or some apparently Chinese RC4558 clone with TI markings. Maybe the latter can be had with NXP markings too, dunno.
NE5534 - those at least can be had with Philips markings which tend to be actual Philips, but I have also seen "NXP". In both cases, recycled. One Philips even had a ripped-out via still soldered to its pin.
LM4562 - usually NE5532 inside.
Burr Brown parts - to the first approximation, all are fake
Zeptobars has pics of TL051 sold as OPA2134 and some AD part as OPA627, I have a fake OPA2604, no idea what it really is but it doesn't meet the spec.
Also, watch out for transistors made by "second source" vendors like InChange Semiconductor Company (ISC) or SavantIC Semiconductor. In theory it sounds nice, it practice they are crap which barely meets "minimum" specs and isn't even rated for things like SOA at all.
Some sellers may lie and say they sell brand name transistors while actually sending those "replacements". And of course there is a whole market of transistors with false markings.
I generally advise to avoid anything from this list because once a counterfeit part is available, it drives real ones out of the market thanks to lower price.