Harems known to me:
Ai yori Aoshi
Angel Tales (Tenshi no shippo)
Comic Party
DearS
Dual
Fate/stay night -- anime has harem downplayed, so mostly Saber and Rin
Futakoi (I haven't seen F.Alternative)
Hanaukyo Maid Tai (both versions)
H2O (abusive lead)
Kanon (both versions)
Maburaho
Magikano
Mahoraba (if we count Kozue's alts as persons)
Martial Successor Nadesico (scroll down)
Nagasarete Airantou
Natsuiro no Sunadokei OVA
Ranma
RahXephon -- some said the main story is how Ayato kills members of his harem
Sekirei
Shuffle
Tenchi Muyo
To Heart -- downplayed in anime to triangle of Shiho vs. Akari, but still
Toradora (counted as 3-way for Taiga, Ami, Minorin)
true tears
Zero no Tsukaima
Extra triangles:
ef (Miyako vs. Kei)
Kimi ga Nozomu Eien / Rumbling Hearts
Macross Frontier (Ranka vs. Sheryl)
Midori no Hibi (Ayase vs. Midori)
Myself;Yorself (Nanako vs. the nice girl extra)
Excluded:
Crescent Love -- based on eroge with siscon, but the anime is NOT a harem
Keitai Shoujo -- direct map of eroge
Harems I heard about but not seen:
Clannad -- only watched an episode and half
Tayutama -- incomplete at the time of this writing
Yumeria (according to a post at Chizumatic)
Kannagi -- quit it before other girls showed up
REMINDED by readers:
Love Hina (by tudza). BTW, I didn't complete it and never learned who the promised girl was (if she was even included into the harem). Da Capo (by JTfish) -- did not watch. Asu no Youchi (by nobody) -- did not watch.
UPDATE: It just occured to me that if you like harems, under no circumstances you should go down the list above and watch them all; some are bad enough that even pirating them would be a loss of time (e.g. H2O, Nagasarete Airantou). Do your research. Start with the ones in bold at least.
UPDATE: New additions: Kage Kara Mamoru -- in rejects pile Gift -- I actually blogged Miao's mocking of it Tokimeki Memorial Hand Maid May -- special case of ugh Negima -- way too long, is a reject anyway (Shinbo version)