Novel Experience
Sometimes you just gotta go slumming. And when the advanced races log into the human BodyNet, they can feel what it feels likes to be a human going about their lower life-form day via a full-body sensory suit that broadcasts every nerve impulse to voyeuristic subscribers to A-Fans. This is like the "Art & Culture" answer, except that the humans aren't trying to create art, per se. Rather, they are the art.
What human wouldn't like to experience a day in the life of a dolphin? Or a lemur? Or a peregrine falcon? It's kinda like a human safari, but from a first-person perspective! Of course, fans can tap into 3rd-person cams all around the city/countryside so they can live the life from any angle desired.
If humans like to dress up as furries, who's to say that aliens don't like to dress up as nakies?
Black Market
Of course, once you've had a taste of walking around in a people suit, some will want to indulge their darkest urges and take it to the logical conclusion: full bodily control. This requires special suits which not only broadcast sensory signals, but also impose motor signals onto the wearer, turning them into a literal skin puppet. Various Human Rights groups across the galaxy argue that this sick experience is beyond the virtues of upstanding aliens, but obviously not all aliens feel the same way.
And nothing is particularly special about humans. The aliens do the same thing to every other life form on Earth. Nor do they respect the species boundaries that are deeply ingrained in human taboos...you can make this as dark as you like.
Test Subjects
If the other species are DNA-based, then perhaps humans make good in vivo test subjects for drugs and medicines. We could be the literal lab rats for a higher civilization. They may even make Earth habitats which closely reflect some of their own communities so that humans living there would be as biologically similar to the aliens as possible. Of course, humans would always have to sign up for such experiments voluntarily, but the superior alien entertainments make this a trivial problem to solve. Humans and their sugar water have nothing on alien scientists.
If the aliens are sufficiently advanced, they may be able to preserve human mental states, perform invasive/destructive experiments on humans, and then restore them to a pre-surgical state. They don't do this on themselves because there is a small risk of failure that they are not willing to assume. But the lower human castes accept this trade eagerly.
Travelling Zoo
Why limit the human freak show to Earth? Plop a community of human "explorers" into an alien FTL ship and send them on a tour of planets for all the locals to gawk at. Humans get the road trip of a lifetime, and aliens don't have the leave the comfort of their home to get a look at the last uncontacted species in the galaxy. Compensation for the humans is trivial (equivalent to shiny baubles to the aliens), but the Circus Ringleaders make out like bandits.
Gofers
Long-term the novelty will wear off for most aliens. Then what? Will humans be ignored? Neglected? Exterminated? Nope. They will be put to use. Aliens who have populated the entire galaxy know one thing extremely well: how to specialize into a niche. Every species exists in harmony because a balance has been achieved whereby every species contributes something useful to the galactic economy. Every species represents a tradeoff in size, strength, intelligence, resource demands, resilience, etc. And for each combination of attributes, there is some job, somewhere in the galaxy, where that is the optimal combination.
For humans to exist in this galaxy long-term, they will have to split up into smaller bands and fill these niches on thousands of worlds, asteroids, and space stations, just as aliens will come to earth and colonize and fill niches there, crowding out the less efficient humans. There is no malice or dark overtones of wiping out the human race: just ruthless pragmatism and extreme demand for efficiency. Since humans aren't the smartest, strongest, biggest, smallest, or most durable of any species, they will tend to be a roving jack-of-all trades which specializes in helping out exactly in the time and place they are needed, and having the flexibility to do so competently (that is, better than the other species which are ruthlessly specialized to most of the existing niches). They won't be the best at anything, but they will be better than average by virtue of their lack of over-specialization. Which means they won't be wanted forever, but they will be wanted when a disaster or upheaval creates a local vacuum that can be filled by a particular roving band of humans.