They could be monitored if the government had surreptitiously gained access to Google servers or internal data transfers by compromising infrastructure such as Google's datacenter-to-datacenter links.
I use that example because I recall a leak (IIRC, either as part of or contemporaneous to early rounds of the Snowden leaks) that the NSA had done exactly that with unencrypted inter-data-center links of Google and other entities with multiple datacenters, and reports shortly after that that Google and several others had taken action to secure and encrypt those links afterwards.
https://en.wikipedia.org/wiki/MUSCULAR_%28surveillance_progr...
That was the famous slide that showed where Google took off SSL with a little smiley face--which reportedly caused Google engineers to "explode with profanity."
The NSA actually did not do the actual hacking. The British GCHQ did, with technical assistance from the NSA. Thus the NSA could pretend that since the GCHQ collected all the information, it was foreign-sourced and therefore not subject to FISA court jurisdiction.
"Honey, why do searches for 'man date' and 'man find' appear in your your internet history?" - My future wife.
…still not as bad as O_CREAT though.
It's just displaying this: https://www.google.com/trends/hottrends/visualize?nrow=5&nco...
Also, even if Google is fully HTTPS, if a query returns images hosted on unsecured websites, those urls will be plainly visible and hence implicative.
Edit: The embedded thumbnails are actually encrypted as pointed by the comment below.
Do they hand it over to law enforcement/NSA/oppressive regimes? Maybe.
For Mirimir, they have no clue. Just a bunch of blind alleys.
https://www.theguardian.com/technology/2013/nov/18/uk-us-dar...
¹ I have no reason to doubt this is true, but AFAIK the only evidence is that Google said it would be, in response to NSA/GHCQ's MUSCULAR program.
I showed ruinmysearchhistory.com to a Pakistani Muslim friend, not having clicked it myself, and he thought it was funny until the ISIS application parts started coming up, when he consequently freaked out, as you might imagine.
But this got me wondering -- it seems to be widely accepted that googling things like "how to make a bomb," "bomb materials," "where to buy guns," etc will get you put on a government watchlist.
It's never been clear to me whether this is superstition or if there's truth to it. Google is fully HTTPS-- how could your searches be monitored unless google was handing them over to the government?