I need to catch up on Again!!; it stopped getting scans for several years. But it's really good, and even has an English release. To my recollection it never comes close to being a harem; there are a bunch of girls but no actual romantic entanglement with the protagonist (besides maybe the main girl).
I also recommend Moteki by the same author; it's got a similar feel (pathetic guy trying to improve himself and his social life), but with no supernatural elements. It's refreshing in that the harem premise is a facade and it's not about teenagers. It's got great characters and a good feel; the only problem is that I've heard it goes in strange places in the second half (I haven't finished it yet).
In another similar vein to Again!!, I started reading
"Umareru Kachi no Nakatta Jibun ga Anna no Tame ni Dekiru Ikutsuka no Koto" recently. I went in mostly blind; it also features a loser protagonist who goes back in time and gets to re-live his life. The catch is that the protagonist is a complete piece of irredeemable s***. Things get dark, fast.
Official King of PotD
You only need one T-Rex to make the point, though. ~ Samus Sedai