user11144: Offhand, I say the Shepherd's Mate. But let us just consider "serious" tournament play. Still, the game must be rather short to be repeated extremely often. Could be a "Will they ever learn" opening trap or a prearranged draw line. Anyone care to research it in a megabase?
Note that just because Lichess lists 187×10^6 e4 vs. 100×10^6 d4 doesn't mean that an e4 game will be the winner! (By playing always the most often played move on the analysis board, I landed in the Lasker Pelikan Sveshnikov.)

user3757: The most played game: a drawing line
The most played game in the TWIC database (issues 920 to 1438, containing about 1.8 million tournament games) is the following one, which appears 111 times. I add also a variation of the same (a change in move order) that is the second most played game (87 times). A couple of variations ending a move earlier or a move later also are amongst the most played games, with 38 and 39 repetitions respectively.
[FEN ""]
1.e4 e5 2.Nf3 Nc6 3.Bb5 Nf6 4.O-O Nxe4 5.d4 Nd6 6.dxe5 Nxb5 7.a4 Nbd4 8.
Nxd4 Nxd4 ( 8...d5 9.exd6 Nxd4 10.Qxd4 Qxd6 11.Qe4+ Qe6 12.Qd4 Qd6 13.Qe4+
Qe6 14.Qd4 Qd6 {2nd most played game, 87 times} ) 9.Qxd4 d5 10.exd6 Qxd6 
11.Qe4+ Qe6 12.Qd4 Qd6 13.Qe4+ Qe6 14.Qd4 {15th most played game, 38 times
} 14...Qd6 {Most played game, 111 times} ( 14...Qd6 15.Qe4+ {14th most 
played game, 39 times} ) 1/2-1/2

How I found the answer
In case anyone is interested, I used a custom made script to parse the games in pgn format and extract the movetext section (the section containing the actual moves and result).
After saving the results as a dataframe in R, I grouped the data by the column movetext (equal games are grouped together), calculated the number of times for each game and sorted in decreasing order:
    games <- mdata %>% group_by(movetext) %>%
        summarise(n_times = n()) %>% arrange(desc(n_times))

And I only took into account the games where there was at least one move by each of the players. Otherwise, the most played game would be "0-1", black wins because white didn't show up, followed by "1.e4 1-0", white wins because black didn't show up.

11144: <p>Offhand, I say the Shepherd's Mate. But let us just consider &quot;serious&quot; tournament play. Still, the game must be rather short to be repeated extremely often. Could be a &quot;Will they ever learn&quot; opening trap or a prearranged draw line. Anyone care to research it in a megabase?</p>
<p>Note that just because Lichess lists 187×10^6 e4 vs. 100×10^6 d4 doesn't mean that an e4 game will be the winner! (By playing always the most often played move on the analysis board, I landed in the Lasker Pelikan Sveshnikov.)</p>
 3757: <p><strong>The most played game: a drawing line</strong></p>
<p>The most played game in the <a href="https://theweekinchess.com/twic" rel="noreferrer">TWIC</a> database (issues 920 to 1438, containing about 1.8 million tournament games) is the following one, which appears 111 times. I add also a variation of the same (a change in move order) that is the second most played game (87 times). A couple of variations ending a move earlier or a move later also are amongst the most played games, with 38 and 39 repetitions respectively.</p>
<pre><code>[FEN &quot;&quot;]
1.e4 e5 2.Nf3 Nc6 3.Bb5 Nf6 4.O-O Nxe4 5.d4 Nd6 6.dxe5 Nxb5 7.a4 Nbd4 8.
Nxd4 Nxd4 ( 8...d5 9.exd6 Nxd4 10.Qxd4 Qxd6 11.Qe4+ Qe6 12.Qd4 Qd6 13.Qe4+
Qe6 14.Qd4 Qd6 {2nd most played game, 87 times} ) 9.Qxd4 d5 10.exd6 Qxd6 
11.Qe4+ Qe6 12.Qd4 Qd6 13.Qe4+ Qe6 14.Qd4 {15th most played game, 38 times
} 14...Qd6 {Most played game, 111 times} ( 14...Qd6 15.Qe4+ {14th most 
played game, 39 times} ) 1/2-1/2
</code></pre>
<p><strong>How I found the answer</strong></p>
<p>In case anyone is interested, I used a custom made script to parse the games in pgn format and extract the movetext section (the section containing the actual moves and result).</p>
<p>After saving the results as a dataframe in R, I grouped the data by the column movetext (equal games are grouped together), calculated the number of times for each game and sorted in decreasing order:</p>
<pre><code>    games &lt;- mdata %&gt;% group_by(movetext) %&gt;%
        summarise(n_times = n()) %&gt;% arrange(desc(n_times))
</code></pre>
<p>And I only took into account the games where there was at least one move by each of the players. Otherwise, the most played game would be &quot;0-1&quot;, black wins because white didn't show up, followed by &quot;1.e4 1-0&quot;, white wins because black didn't show up.</p>
