Here is my best argument against the simulation hypothesis:

Simulations typically have a reduction in dimensionality, at least the ones we have made so far. Which is to say: you cannot simulate the whole of the universe within itself. Our simulations are more granular and smaller than the real world, even if they become remarkably close. This reduction in detail can be temporal or spatial.

The simulation hypothesis supposes that the number of simulations would be astronomically high because of recursive simulations in simulations. This is the part that I take issue with. Assume that we live in simulation level X (some point in the chain of simulations). Anything that happens in the simulation X+1 (the simulations we make) would need to be computable by a set of operations in simulation X. This is similar to how a virtual machine ultimately runs as CPU instructions on the host machine.

This means that Simulation X bounds the complexity of every nested simulation (Simulation X+1...X+∞). If you run a virtual machine A inside a virtual machine B, on physical host C virtual machine A is still expressible as a computation of the host machine. You cannot create a virtual machine with higher specs and have this run in real-time, since the complexity of this chain is bounded by the root node.

Note that there is also overhead with every layer of simulation. Our entire universe is not interested in running simulations, only a small fraction of the compute under the control of intelligent life. A god-like civilisation that has conquered the universe may be able to dedicate a significant portion, but this necessarily cannot be 100%. 

This means that the number of simulations should be much more finite than typical formulations of the simulation hypothesis depict.

This does not mean that I rule the possibility out. Even if the chain is short there may be many simulations which we could exist in. We might be the only simulation. But this possibility seems no more profound or likely than any other unprovable statement.

The best response I've heard against the simulation hypothesis is "If we're simulated, why aren't we asked to do meaningful work?" Think about why we would want to simulate personalities in our near to medium term future: to answer questions, to help us work faster, to entertain us, to be our companions, etc.

So why aren't we asked to complete the equivalent of Mechanical Turk questions? Is compute is so unfathomably cheap that they there's no economic reason we would need to "pay rent" so to speak? Even if that's the case, why don't our creators want to interact with us directly? In other words, if we're all video game characters, who is the player character? Why do I have consciousness, if I'm just an NPC?

And on and on. The crux is whether you believe that in the world that allows us to be simulated, it's more likely that our creator just wants to view us through a thick pane of glass than they'll want to play with us. My intuition is very much on the later.

I've been checking Joscha Bach's blog these days, and I had found this blog post on the topic which I think goes to interesting depth on the question: 

Do we live in a simulation?

Here's an attempt:
(1) Maybe by default simulations aren't conscious. You have to go out of your way to make a conscious being, e.g. maybe it has to be biological or something fancier than whatever the most efficient-yet-accurate simulation would be.
(2) Also, maybe there are pretty universally enforced ethical prohibitions against going out of your way to make conscious beings and then putting them in such a nasty horrible situation as 21st-century Earth. The number of entities with the will & means to violate this prohibition is vanishingly small, small enough that any conscious simulations created by them are outnumbered by the conscious non-simulations / evolved creatures like us.