I had speedfan 4.49 running in the background with all charts enabled. Then I did a play through of the Doom demo on medium settings. But I stopped midway through the demo because I thought I smelled burning plastic. My Geforce 760 GTX reached a temperature of 80C while the rest of my components never went above 40-52C. Is that safe?

Clean all fans and filters

Sounds like the smoke that keeps electronics running is coming out

Those temperatures shouldn't be a problem (though highest my system's components get is 60C), probably just some dust causing the smell, so like said, clean fans and heatsinks.

I smelled burning plastic/rubber from my computer back in early 2004. Turned out that the fan in the PSU had stopped working so the PSU got really hot.

I stopped using it and ordered a new PSU right away.

Open your PC and inspect all the components inside. (actually try to figure out what kind of components seems to smell like that)

Usually, a burning smell could be related to the CPU, the GPU, the mobo (the northbridge chip could be the cause for example), and as Freddo stated above, the PSU as well.

And lastly, it wouldn't harm to look for any swollen capacitors (on your mobo) as well.