1) Yes, some Korbanos do not require Zerikah. Instead they require "Shefichah" -- the blood is poured on the base (Yesod) of the Mizbe'ach. See Zevachim 37a, where Rebbi Yishmael derives from the verse, "... and the blood of your sacrifices shall be poured" (Devarim 12:27), that the blood of the Korban Pesach should be poured. The Rambam (Hilchos Ma'aseh ha'Korbanos 5:17) rules that Bechor, Ma'aser, and Pesach all require Shefichah, not Zerikah.

2) I found, bs'd, another example where a Korban is acceptable without Zerikah.

This is based on the Gemara in Zevachim 85a where Ula said that if the inner parts ("Emurim") of offerings of Kodshim Kalim were brought onto the Mizbe'ach before Zerikah was performed with the blood, they are no longer removed from the Mizbe'ach because they have now become the "bread" of the Mizbe'ach. The Rambam (Hilchos Pesulei ha'Mukdashin 3:12) rules in accordance with this Gemara.

The Kesef Mishneh there writes that even though the Emurim were put on the Mizbe'ach in the wrong way, since the blood was sprinkled afterwards on the Mizbe'ach the Emurim may now remain on the Mizbe'ach. However, several Acharonim (see Sefer ha'Mafte'ach in the Frankel edition who cites quite a list) disagree with the Kesef Mishneh and maintain that even if Zerikah was not done, the Korban still is not taken down from the Mizbe'ach. One of these Acharonim is the Chafetz Chayim, in his Sefer Likutei Halachos (85a, Zevach Todah, DH Eimurei). He writes that it is obvious that if the blood was later sprinkled, then the Korban is valid, since it should make no difference how it was put on the Mizbe'ach in the first place as long as the Zerikah was done correctly afterwards. Therefore, Ula's Chidush must be that even though Zerikah was never done, nevertheless the very fact that the Korban got onto the Mizbe'ach is sufficient to make it acceptable b'Di'eved. The Chafetz Chaim concludes that even if the blood spilled on the floor after the Korban was placed on the Mizbe'ach, since the blood was still there when the Korban was put on the Mizbe'ach, this is sufficient. At that time he could have sprinkled the blood, so it follows that the Mizbe'ach received a valid Korban.

3) I think I have found another unusual example of a Korban which can be acceptable even without Zerikah.

This is the scenario of a Mizbe'ach not in its proper place. See Zevachim 59a, where Rav Gidal said in the name of Rav that if the Mizbe'ach was uprooted from its place, one may burn the incense at the original place of the Mizbe'ach. See also Tosfos to Zevachim 61a (on the last lines before the lines get wide), who writes that it is not only incense that one may burn even though the Mizbe'ach is not there, but one may also burn the inside parts of the animal ("Emurim") at the original place of the Mizbe'ach.

If we now go back to Zevachim 59a, we see that Rava stated that even though one may burn the incense without a Mizbe'ach, Rav agrees that one may not sprinkle the blood. Rashi explains that one may offer blood only on the Mizbe'ach.

It follows that even though one needs the Mizbe'ach in order to sprinkle blood, according to Tosfos (61a) one may burn the parts of the Korban on the Mizbe'ach. This would mean that a Korban is acceptable even though the blood has not been sprinkled on the Mizbe'ach.

Kol Tuv,

Dovid Bloom