user3237: I am looking for some puzzles where there is a forced mate in as many moves as possible (ideally 20 or more). Yet the puzzles need to be as easy as possible!
You will probably need to find some puzzles where the defending side has a lot of spite checks to delay the mate.
.
Edit :
I just made a very easy mate in approximately 23. White to move:

It's really really easy since Black can do nothing. But it doesn't totally satisfies me since the position is of course not legal...

user8860: Here's an easy mate in 20 with a unique solution
(which becomes a very easy mate in 19 after the first move):
[Title "Noam D. Elkies, Chess Stack Exchange 2020"]
[FEN "6bn/p4p1k/p4Ppp/p7/p3K1P1/P4N2/1P6/7n w - - 0 1"]


user3405: There are many:
     [Title "Mate in 20"]
 [FEN "3K1B2/1p6/pp6/rk2N3/b1p5/1pP5/1P2P3/8 w - - 0 1"]

You should search puzzles from the 1900. It was a golden era for chess puzzles. I found a mate in 63 some days ago. 
Chessmaster also has a nice collection of interesting(and long) puzzles. There are many sites where you can sort puzzles according to difficulty and turns to mate, but I can't remember any atm.

user15543: I present unto you a superbly easy mate in 21 that I found the other day in the Matplus.net forums. Give it a try!
[Title "Filip Bondarenko, Feenschach 1960, Mate In 21"]
[FEN "8/7Q/2r1p3/2rkr3/2rrr2Q/7K/8/8 w - - 0 1"]

This is a mate in 24 that I quite like. You can view the solution in Yet Another Chess Problem Database.
[Title "Martin Hoffmann & Franz Lutsenberger, Schach-Almanach 1977-1978, Mate In 24"]
[FEN "8/7p/6pP/5pP1/pK2pP2/1pBpP3/pn1N4/k7 w - - 0 1"]

Finally, just for fun, here is a legal version of @Fate‘s idea that I have created solely for this answer.
[Title "me, chess.stackexchange.com 8/16/2019, Mate In 20"]
[FEN "6bB/3p1pB1/2pP1Ppr/2P3P1/2p5/2P3p1/5pPk/5Kbr w - - 0 1"]


3237: <p>I am looking for some puzzles where there is a forced mate in as many moves as possible (ideally 20 or more). Yet the puzzles need to be as easy as possible!</p>

<p>You will probably need to find some puzzles where the defending side has a lot of spite checks to delay the mate.</p>

<p>.</p>

<p><strong>Edit :</strong></p>

<p>I just made a very easy mate in approximately 23. White to move:</p>

<p><img src="https://i.stack.imgur.com/LYLEZ.png" alt=""></p>

<p>It's really really easy since Black can do nothing. But it doesn't totally satisfies me since the position is of course not legal...</p>
 8860: <p>Here's an easy mate in 20 with a unique solution
(which becomes a very easy mate in 19 after the first move):</p>

<pre><code>[Title "Noam D. Elkies, Chess Stack Exchange 2020"]
[FEN "6bn/p4p1k/p4Ppp/p7/p3K1P1/P4N2/1P6/7n w - - 0 1"]
</code></pre>
 3405: <p>There are many:</p>

<pre><code>     [Title "Mate in 20"]
 [FEN "3K1B2/1p6/pp6/rk2N3/b1p5/1pP5/1P2P3/8 w - - 0 1"]
</code></pre>

<p>You should search puzzles from the 1900. It was a golden era for chess puzzles. I found a mate in 63 some days ago. </p>

<p>Chessmaster also has a nice collection of interesting(and long) puzzles. There are many sites where you can sort puzzles according to difficulty and turns to mate, but I can't remember any atm.</p>
 15543: <p>I present unto you a superbly easy mate in 21 that I found the other day in the <a href="http://matplus.net/start.php?px=1558655710&amp;app=forum&amp;act=posts&amp;fid=xshown&amp;tid=1610" rel="nofollow noreferrer">Matplus.net forums.</a> Give it a try!</p>
<pre><code>[Title &quot;Filip Bondarenko, Feenschach 1960, Mate In 21&quot;]
[FEN &quot;8/7Q/2r1p3/2rkr3/2rrr2Q/7K/8/8 w - - 0 1&quot;]
</code></pre>
<p>This is a mate in 24 that I quite like. You can view the solution in <a href="https://www.yacpdb.org/#442276" rel="nofollow noreferrer">Yet Another Chess Problem Database.</a></p>
<pre><code>[Title &quot;Martin Hoffmann &amp; Franz Lutsenberger, Schach-Almanach 1977-1978, Mate In 24&quot;]
[FEN &quot;8/7p/6pP/5pP1/pK2pP2/1pBpP3/pn1N4/k7 w - - 0 1&quot;]
</code></pre>
<p>Finally, just for fun, here is a legal version of @Fate‘s idea that I have created solely for this answer.</p>
<pre><code>[Title &quot;me, chess.stackexchange.com 8/16/2019, Mate In 20&quot;]
[FEN &quot;6bB/3p1pB1/2pP1Ppr/2P3P1/2p5/2P3p1/5pPk/5Kbr w - - 0 1&quot;]
</code></pre>
