Which is the densest gas known to exist under normal "shirt sleeve" conditions: room temperature, one atmosphere, won't explode on contact with air, won't kill everyone in the building in trace amounts, etc.
Answer
Perfluorobutane is inert and has almost twice the density of sulfur hexafluoride. It is non-toxic enough that it is used in fire extinguishers and injected as a contrast agent for ultrasound. Boiling point: $-1.7\ \mathrm{^\circ C}$.
Perfluoropentane is similar and rarer but somewhat higher density $(\sim13\ \mathrm{kg/m^3})$ in proportion to its higher molecular mass. Its boiling point is $28\ \mathrm{^\circ C}$ (uncomfortably warm, but your thermostat can go that high). This is the densest gas that strictly meets all the criteria in the OP.
If we relax the criteria a bit:
Perfluorohexane is just over the boiling point limit at $56\ \mathrm{^\circ C}$, but it has a molar mass of $338\ \mathrm{g/mol}$ which makes it slightly denser in gas form than tungsten hexafluoride ($\ce{WF6}$). It's also inert and non-toxic, unlike $\ce{WF6}$.
The ultimate gas density would be uranium hexachloride using depleted uranium and $\ce{Cl-37}$, with a molar mass of $460\ \mathrm{g/mol}$, which makes it over 50 % denser in gas form than tungsten hexafluoride, and 3 times denser than sulfur hexafluoride, but it has a boiling point of $75\ \mathrm{^\circ C}$, decomposes on contact with air, is toxic and slightly radioactive.
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