After releasing fourteen girls from the grasps of runaway spirits by making them fall in love with him, Keima has proven himself to be the Capturing God of both the 2D and 3D worlds! But a new challenge awaits as Diana, the goddess possessing Keima's neighbor Tenri, tasks him to find her siblings, and his only clue to their whereabouts resides with past conquests who still retain their memories. Now Keima is on the hunt in hopes that these divine beings might finally release him from his contract with Hell. But with the shadowy organization known as Vintage out to kill these girls, it becomes a race against time to put a stop to their plans and restore these goddesses to their former power!
Yesterday, Kyon was helping prepare for an SOS Brigade Christmas party. But today, he wakes up to a whole other world. Haruhi and the SOS Brigade are gone, Koizumi's class is missing, Asahina doesn't recognize him, Nagato is still a Literary Club member and even Ryoko Asakura has returned. As the only person who notices that everything has changed, Kyon is left to discover what happened to his friends and figure out if his life truly is better without aliens, time travelers and ESPers.
Both World God Only Knows and Haruhi start out with a ridiculous (in a good way) supernatural premise and a lot of comedy/parody with some lighthearted drama. But there's a point at which things get serious and you realize that the series has been building up to a real arc, and the characters go through some real growth. The series takes on new meaning.
That point is The Disappearance of Haruhi Suzumiya and the goddess arc (Megami-hen) in World God Only Knows. In both cases, you really reeeally should see seasons 1 and 2 first. (It's hard to appreciate the new meaning if you aren't familiar with the old meaning.) Note: If you can, see the OVAs of WGOK, but it's not essential. The anime skipped a lot of the manga regardless. And if you're willing, watch all of the Endless Eight arc in Haruhi; it's not essential but actually does have some relevance.
In any case, Disappearance and Megami-hen are both great if you are invested in the characters. If you're reading this because you liked the way one series started off amusing but then went deeper, try watching the other.