While the original run of the Hey Arnold! TV Series on Nickelodeon may have ended in 2004, re-runs of the show are still occasionally on various channels across the world.
United Kingdom and Ireland
Hey Arnold! is sometimes repeated on the Nicktoons channel on Sky channel 606 (and replay channel 630), Virgin Media channel 717, Smallworld Cable channel 606, UPC Ireland channel 606 and TalkTalk TV channel 320.
United States
As of August 2012, it only airs on Teennick. Here is the schedule for what times it comes on Teennick: Friday Nights at 12 & 12:30AM, and 2 & 2:30AM (repeats of 12 & 12:30AM) Saturday Nights at 1 & 1:30AM, and 3 & 3:30AM (repeats of 1 & 1:30AM) Tuesday Nights at 1 & 1:30AM, and 3 & 3:30AM (repeats of 1 & 1:30AM)
You can also find a few episodes on the Nickelodeon website or typing "hey arnold nick.com" into the search engine Google.
You can also buy the season sets, volumes and complete season on DVD from various web sites.