"The West" is a bit broad, so I'll focus on the US and Germany.
If we look at political parties, the Communist Party USA has not had its own presidential candidate since 1988. The party itself says that its numbers grew because of Trump, but the numbers aren't significant. The Socialist Party USA got 0.0% (4061 votes) in the 2016 election, down from 0.01% (6581 votes) in 2008 and 0.01% (10822 votes) in 2004.
The relatively positive run of Bernie Sanders does seem to signal a desire to move the democratic party to the left, but Sanders is far from being a communist or even a socialist.
The MLPD - a stalinist/maoist party - got 0.06% (24.219 votes) in the 2013 election, down from 0.07% (29.261 votes) in 2009, and 0.1% (45.238 votes) in 2005. The DKP - a maxist/leninist party - did not seriously take part in federal elections since 1983.
Die Linke is a social democratic party, but it has some communist factions. In the 2013 election, they got 8.6%, down from 11.9% in 2009. In current polls, they are down again at 8%.
I'm not that familiar with the situation in other countries, but it seems that the situation is similar in France, where the communist party is generally in a downwards trend (2012 being an exception where it gained votes). The communist party of Austria experienced a slight - but non-significant - rise. The communist party of Ukraine lost significantly since 1999, as did the communist party of Hungary (with a slight but insignificant increase in 2014).