Election polls definitely affect the election results, but the extent is debatable.
Part 1: Study - Do Polls Influence the Vote?
This study analyses how do polls influence voters' decisions by examining the impact of polls on the 1988 Canadian election.
The results shown in panel A of table 1 confirm that voters did respond to the information provided by the polls. The greater the Conservative lead over the Liberals in the most recent poll, the more inclined voters were to believe that the Conservatives had better chances of winning than did the Liberals. The same pattern held with respect to the Liberal versus NDP race.
There is evidence of an interactive effect in the case of the Conservative/Liberal equation: it seems that among poll watchers, and only among them, the propensity to vote Conservative rather than Liberal was related to the gap between the two parties in the most recent poll.
All in all, there are good reasons to believe that the polls had an impact on the vote in the Canadian 1988 election.
campaign pooled data analysis entails examining the vote intentions, expectations, and preferences of our respondents and relating these to the information conveyed by the polls at the time respondents were interviewed
time-series analysis involves analyzing daily patterns in aggregate vote intentions, expectations, and preferences and relating these to the nature of poll information that was available every day of the campaign
panel analysis, uses both the campaign and the postelection surveys. It examines change (or absence of change) between the vote intention indicated during the campaign and the actual vote reported after the election, and it relates this to change between the poll information available at the time the individual was interviewed during the campaign and the information available by Election Day
Note: All text in block quotes are quoted from the study, Do Polls Influence the Vote?, and emphasis is mine.
Part 2 - Reasons
Boomerang / Bandwagon effects
There are basically 2 ways that polls can affect the results:
1. the boomerang effect
This would occur when supporters of a candidate consistently polls far ahead of his/her opponent, thus supporters may not turn out on election day to vote as they assume their candidate will win almost for certain. However, they turned out to be wrong and the race becomes closer than expected.
Without this poll, the candidate who's leading would have won.
An example may be the 2016 US Presidential Election in which Clinton consistently polled above Trump, thus Clinton supporters assume that it's a sure-win for her, resulting in a low turnout rate for Clinton1.
2. the bandwagon effect
This is the opposite of the boomerang effect. Supporters would expect a race to be a landslide for a particular candidate, but polling showed that their challenger is improving in the polls and the election may be a close race after all. This would encourage people to be more inclined to vote.
Without this poll, the challenger would have won.
Also, a research published in 2012 showed that people are in fact influenced by polling:
The researchers asked a selected group of voters to state their opinions on a variety of real public policy questions, and then presented them with fabricated poll results on the same topics. When the test subjects learned that a large number of experts favored a position, opinions shifted by 11.3%. But the "opinions of people like me" changed opinions by just 6.2%, while a general poll saying that a majority of people favored one side or the other moved the needle by 8.1%.
This research is further elaborated in this Huffington Post article:
Researchers generally posit two psychological mechanisms underlying conformity: (1) people’s desire to adopt the majority position so as to feel liked and accepted or believe they share the prevailing opinions of their community (i.e., social acceptance); and (2) people learn from the “wisdom of crowds,” or assume that other people did the research so their collective wisdom indicates something about the quality of the candidate or platform (i.e., social learning).
[ ... ]
polls reveal information about the likelihood of a policy passing or the election of a candidate, so people resolve cognitive dissonance (“Policy X is going to pass, but Policy X makes me unhappy”) by switching to the side they believe is going to win
1This source doesn't actually highlight that the low turnout rate is due to voters being affected by polling. Regardless, it showed that turnout was low.