Just instruments mainly. Rarely amps. Sometimes i'll hear a very obvious effect (like an eventide 910's pitch shift, which is pretty obvious). Can sometimes pick out synths, but there's SOOO many similar ones out there, that it's hard to say.
Truthfully, most of the time even when I KNOW what the gear is, and own the gear myself, I have a hard time saying, "it sounds like this piece of gear" because there's so many other pieces in the chain (plus an artist that's unique sounding). Point in case. My main vocal mic is an AT4060. Apparently it's all over the new Justin Timberlake album, and I'll agree that it sounds similar, but I don't sound like Mr. Timberlake so i'd never have made that connection.
Also, for example, I know that Trent Reznor uses (among every other piece of gear in the world), a Sidstation, a Machinedrum, and a Moog Voyager
in many of his pieces, all of which I own, but I have a hard time telling where he's using what.
That being said, if i don't document my synth sounds for songs that I write, I can rarely remember which synth (software or hardware) it came from. Sometimes it's my guitar going through moog pedals, and I forgot what it was at all.
I don't think that often people even notice the difference between studios. When listening to The White Album, does "Hey Jude" stick out at you immediately as being recorded at Olympic instead of EMI studios? Never noticed it and thought "that sounds like a totally different studio and console". Was somewhat startled to find out how many studios/rooms some of the Beatles albums were recorded in.