He is a fairly rare example in the Japanese manga industry for being one of the most successful and beloved creators of all time, but virtually never writing any manga himself. Even his first serial from the late 80's, Cyborg Jii-chan G originally credited a fake writer despite the fact it was written and drawn by Obata.
This first serial was short-lived but Obata remained working for Weekly Shonen Jump and through the 90's had a number of short-lived series in the magazine that were written by others but none that lasted more than a year.
The series that became his huge mainstream breakthrough was Hikaru no Go (written by Yumi Hotta) and after lasting for six years and twenty-three volumes it has still remained his longest series though every series he has worked on since has been considerably higher profile (even the ones that failed got more promotion than average at the time of their original serialization).
His next major success (which brought him to the attention of Western audiences) was Death Note, written by the mysterious Tsugumi Ohba pen-name who has almost exclusively published work with Obata. Though not long-running, it was a major commercial success (including outside of Japan).
After its end, Obata did a few one-shots with a variety of writers and had another failed serial in Shonen Jump before reuniting with Ohba to create their next major success in Bakuman. (which ran longer than Death Note).
After Bakuman. ended, a short adaptation of the popular All You Need is Kill light novel was released and another failed serial in Shonen Jump went by before Ohba and Obata reunited for a third series, Platinum End which ran in the new magazine of Jump SQ.
Obata's popularity in the US is rather notable in that since the rise of Death Note, he has gotten preferential treatment from publishers. A number of his series have specially been released the same-day digitally as they come out physically in Japan and generally all his work is translated whether it succeeds in Japan or not.