I've been thinking, could there possibly be an organism that is based on the element of helium? If yes, what would it look like? (Images are welcome)
Helium is a noble gas, thus it's very unrealistic that such an lifeform exists.
However, Helium can react if under extreme pressure and temperatures,
and therefore, if any Helium based life-form existed, it would (most likely) live under extreme conditions (high temperatures and pressure) like for example in the sun or deep inside gas giants like saturn and jupiter (at both places there is not just much temperature and pressure but also helium and hydrogen so the HeH+ could be created there).
I also think that if such a lifeform existed it would be a sort of "gas cloud" that can be splitted, squeezed etc. without taking damage because of the extreme conditions it would live in.
Anyway, I don't think such lifeforms exist anyway.
And if they existed, we wouldn't notice because we couldn't meet them anyway (with today's technology).
Helium is a noble gas.
This means its reactivity toward other elements is practically null, so small that even its molecules are mono-atomic.
Life as we know it is based on several molecules formed by joining a small variety of atoms (Carbon, Nitrogen, Hydrogen, Phosphorus, Oxygen among them), reacting among them.
On the base of this premises, it is clear that helium is not a good candidate as base molecule for an organism.
As others have pointed out, Helium is a noble gas, so does not act the way we think of when we think of "Carbon based lifeforms."
A helium based lifeform would be so far removed from what we think of as life that one would have to seriously question what it means to be "alive." We don't have a complete constructive definition for what that word means. Philosophers keep digging at it every generation. We've got some common traits that we think a living creature should have (such as reproduction and metabolism), but even those concepts get fuzzy when you go all the way out to where a helium based creature would be.
So my general answer would be "I can't tell you whether a helium creature can even exist until you pick a definition of 'alive.'" However, practically speaking, I'd be surprised if humanity would recognize such a creature as alive if it were to observe the creature. It would have to be too alien.
But if we achieved a level of peace and enlightenment on par with, say, the Nox from Stargate SG1, then I would only hope that we revisit those assumptions, and give those little balls of Helium the respect they may deserve.
A particularly dense puff of cloud within a helium nebula, massive enough (or with a massive enough object at its core) that its own gravity stirs currents in the molecules of gas and dust from which it's formed, could resemble a living entity distinct from its surroundings. The forces holding it together, the interactions between its constituent elements, would need to form a stable system that naturally changes function or behavior as the conditions in the organism's external environment and internal state develop, and those systemic reactions would need to naturally lead to the preservation of the system. In other words, the cloud and its currents would need to remain relatively unchanged if some solar breeze blew through them, and whatever material is spent or lost by the processes within the cloud would need to be neatly replaced by material newly encountered in and drawn from its surroundings. It might be possible for such a system to naturally tend to become divided into multiple instances of the same stable system under the right conditions, and this might be considered replication. It's unlikely any more sophisticated features of life than these could develop in such a system.
Consider however that this would all be happening on a scale of space and time outside of the reach of human experience. Even the densest nebulae are so dispersed in space as to be practically invisible to the human eye up close, so this "creature" would have to be observed from relativistic distances. And because matter, even the dust in those gravitational currents, moves at a near-infinitessimal fraction of the speed of light, those movements over such great distances would cause just one pulse of whatever constitutes this creature's heartbeat to outlast a human life. It would take humankind generations of close observation just to realize this particular wisp's peculiarity.
And even then, most would just call it a funny cloud.