user15478: I am currently under the impression that White players are allowing the Nimzo-Indian more and more, whereas before they were dodging it via 3. Nf3.
I wanted to check if that is true, but usually databases do not contain this information explicitly. Are there any resources (software or websites) that have this feature?

user12629: SCID's Opening Report shows some statistics which may be useful here. From a given position, one of the things it does is generate a table which shows what moves are common from a given position:
4.2 Moves from the report position
    Move   ECO       Frequency    Score  AvElo Perf AvYear %Draws
 1: Nf3    E10a     8561: 50.8%   56.1%  2622  2665  2009   56%
 2: Nc3    E00d     6495: 38.5%   55.6%  2607  2654  2008   54%

The "AvYear" column there shows the average year in which the move was played.
And another table looks like this:
1.4 Current popularity

Year               1800-99 1900-49 1950-69 1970-79 1980-89 1990-99 2000-09
Once every X games   ---     24      19      13       6      33      12   

Frequency in all years:   once every 12 games
In the 10 years to today: once every 13 games (down 7% from all years)
In the  5 years to today: once every 12 games (no change from all years)
In the  1 year  to today: once every 0 games (no change from all years)

which seems like it would be useful.

15478: <p>I am currently under the impression that White players are allowing the Nimzo-Indian more and more, whereas before they were dodging it via 3. Nf3.</p>
<p>I wanted to check if that is true, but usually databases do not contain this information explicitly. Are there any resources (software or websites) that have this feature?</p>
 12629: <p>SCID's Opening Report shows some statistics which may be useful here. From a given position, one of the things it does is generate a table which shows what moves are common from a given position:</p>
<pre><code>4.2 Moves from the report position
    Move   ECO       Frequency    Score  AvElo Perf AvYear %Draws
 1: Nf3    E10a     8561: 50.8%   56.1%  2622  2665  2009   56%
 2: Nc3    E00d     6495: 38.5%   55.6%  2607  2654  2008   54%
</code></pre>
<p>The &quot;AvYear&quot; column there shows the average year in which the move was played.</p>
<p>And another table looks like this:</p>
<pre><code>1.4 Current popularity

Year               1800-99 1900-49 1950-69 1970-79 1980-89 1990-99 2000-09
Once every X games   ---     24      19      13       6      33      12   

Frequency in all years:   once every 12 games
In the 10 years to today: once every 13 games (down 7% from all years)
In the  5 years to today: once every 12 games (no change from all years)
In the  1 year  to today: once every 0 games (no change from all years)
</code></pre>
<p>which seems like it would be useful.</p>
