Originals, likely finished

Recent
https://en.wikipedia.org/wiki/Tsuritama -  Comedy, Sci-Fi, Slice of Life, Sports - 2017.

https://en.wikipedia.org/wiki/Tweeny_Witches - latest 2007.

https://en.wikipedia.org/wiki/Speed_Grapher - anime finished before manga in 2005, but anime came first.

https://myanimelist.net/anime/1192/Kakurenbo - ended 2004.

Old
https://en.wikipedia.org/wiki/Blue_Gender - ended 2000, so did manga but anime began in 1999.

https://myanimelist.net/anime/1136/Betterman - ended 1999, but is related to two other series.

https://myanimelist.net/anime/4723/Seishun_Anime_Zenshuu - specials ended in 1997.

https://myanimelist.net/anime/4680/Bocchan - novel in 1906, anime ended 1980.

https://myanimelist.net/anime/4339/Ashita_e_Attack - ended 77.

On-going
https://en.wikipedia.org/w/index.php?title=Hoshiai_no_Sora - ends likely in 2019.