I''s Pure

Standalone OVAs from 2000-2009.
Eve no Jikan is labeled on MAL as an ONA, but won the OVA Category during the 2010 Tokyo Anime Award.
There are potentially other OVAs that are labeled as ONAs that aren't included in this list.

Others notable Non OVAs included:
Halo Legends is an ONA.
Mizu no Kotoba is a special.
Interstella5555: The 5tory of The 5ecret 5tar 5ystem is a music video.

Animes With Great "Plot"... These are some of the best Ecchi, Erotica animes...

Buzz was a Spanish subscription television channel produced by AMC Networks International Iberia. Its programming focused on horror content, both in current series and movies.

Despite not being Spanish, I have managed to appreciate the content that this channel transmitted along with several of its dubbings into Castilian Spanish, which, from my point of view, are mostly worth it.

Part 1: https://myanimelist.net/stacks/35192

Part 3: https://myanimelist.net/stacks/35194

Anime that either has a lot of fanservice, or is classed as ecchi or erotica.

Anime series that covers all of the original source they're based on, with some notes.

Part 1: https://myanimelist.net/stacks/16812
Part 2: https://myanimelist.net/stacks/19939
Part 3: https://myanimelist.net/stacks/20122
Part 4: https://myanimelist.net/stacks/20258
Part 5: https://myanimelist.net/stacks/20709
Part 6: https://myanimelist.net/stacks/20940
Part 7: https://myanimelist.net/stacks/21451
Part 8: https://myanimelist.net/stacks/21523
Part 9: https://myanimelist.net/stacks/29835
Part 10: https://myanimelist.net/stacks/35847
Part 11: https://myanimelist.net/stacks/39870
Part 12: https://myanimelist.net/stacks/41719
Part 14: https://myanimelist.net/stacks/46685

OVAs made in the 2000s and beyond that carry on the spirit of the 80s/90s OVA -- a fun, standalone story told in a short amount of time, supported by great production values.

All OVAS,ONA,Special, TV Special with Opening for AMQ, Famous or not!

(Openings being single, not part from TV series)