In my opinion, cries tend to be the most memorable when they manage to capture the personality of the Pokemon in a way that suits their design and background. A distinct melody and rhythm goes a long way in conveying the mood and personality of the Pokemon, as it "humanizes" the cry and makes it easier for us to relate to it. Here are a couple of my personal favorites:
Oddish
Cubone
Sudowoodo
Litleo
Rockruff
I realize that most of my favorite cries belong to unevolved Pokemon, which might be due to the tendency of their evolved forms to lean towards unpaced and high-pitched "animal sounds" which remain generic and unpersonal, the prime example of this being Lycanroc.
Unfortunately, most of the updated cries in Generation 6 followed the same trend in an effort to make the older cries fit in better with the new games. While I can appreciate that the updated cries sound a lot more organic and varied, many of them lost their original elan and personality by having their melody and rhythm watered down and distorted. Which really seems like a missed opportunity to me, since the Psyduck line clearly demonstrates how the new technology could instead be used to complement and enhance the original essence of the cries.
----------
On a final note, Pokemon Diamond was my first game, and many of the early game Pokemon's cries made a lasting impression on me, be it for the reasons mentioned at the beginning of this post or simple due to nostalgia. In any case, here's a little extra that I'm sure all of you Sinnoh trainers will enjoy: