What plant would make us excited and giddy, or at least work on our neurochemical receptors the same way catnip does to cats? Cannabis?
Coca leaves or coffee fruit. (I assume you’re talking about a primitive situation of some kind, no processing or preparation allowed.)
Those’ll both affect any animal, though, right? Is there anything that dopes up humans and only humans, like catnip does for cats?
Actually studies have shown that catnip is like marijuana to primates. Approximately 66% of cats are born with the chemoreceptors for catnip, just as humans have chemoreceptors for marijuana and opiates. Trust me, I am a biologist AND a cat lady!
I may be missing something here, and maybe I don’t get out enough, but people on pot don’t seem to me to be excited or giddy.
Catnip has had a wide range of observed effects, from nothing, to sleep, playfulness, to ecstasy.
So my take on it is sex would be fill in the blank for primates.
But bananas are proven to contain serotonin, right?
Sometimes they get paranoid, though. As long as we’re dealing with such loosely analogous effects, that could be considered the analog for the excited cats. As kanicbird says, catnip has a variety of effects on cats, and the effect may vary from cat to cat, or even different doses for the same cat. I’ve seen cats go into a very stoner-like mellow haze.
“Whoa, man, have you ever, like, really looked at your paw? My claws retract…that’s so cool…”
So I can get high on catnip? Looks like Willy will lose his toys.
Also, SWIM feels drunk with no dizziness while smoking weed.
Cats, in their unintoxicated state, don’t behave exactly like sober humans, so the baseline is different - so we’re already dealing with a quite inexact analogue, before any effect is applied.
Cilantro.
You haven’t been getting out enough, the point is that there are different grades of marijuana that can give you different effects. I thought everyone knew that. 
Also, excited and giddy tends to happen more often to younger, newer users of weed but maybe that’s because traditionally they have had access to better strains and more variety due to there social circles being more diverse (say the freshman dorm experience). 
Axe Body Spray. Or at least that’s what their marketers have convinced teenage boys.
That’s a snarky answer, but not entirely silly. Catnip has a chemical that mimics a male cat pheromone. It binds to an olfactory receptor, not neuronal receptors that are the target of so many human drugs. For female cats in heat, catnip triggers sexual behaviors. For male cats, it triggers competitive and aggressive behaviors. In neutered males and spayed females, it triggers a confusing mashup of all those behaviors.
If you want to be precise about the biochemistry, humans don’t have any pheromone or drugs that behave in a similar way. There is scant evidence of any human pheromones at all, and certainly none that produces a reaction as strong as catnip. Such a “humanip” would cause females to tear off their clothes and males to get in fights. Which seems to be exactly how teenage boys imagine Axe works.
I have observed different effects of different sources (grades?) of catnip as well. Perhaps it is because some is older then others or other storage issues, but I have thrown away certain ones that don’t seem to please my cat as well as others.
Cannabinoid receptors. Chemoreceptors would let you smell and taste the pot, but not affect your behavior as much until it gets into your brain. Yes, they’re detecting the cannabis chemicals, but only in the synapse.
It’s funny with multiple cats: we have 2 or 3 who go crazy for catnip. Another follows along. He doesn’t know why they like it, but there must be something there so he might as well pretend.
I have been told (and no, this is not an “I’m asking for a friend” situation; I’ve never known the difference myself) that indica-based strains make you relaxed, and sativa makes you more alert. Cannabis contains many different chemicals, and relevant here is the ratio of THC:CBD, being higher in sativa.