The answer to this question can be classified in the following manner.
1. the organs which can be removed in Toto without any ill effect.
2. the organs which require some supplements after removal.
It is also presumed that the life span is not altered.
Now category 1. the list is as below-
one eye
Teeth- Not all but may be incisors, otherwise dentures would be required.
clavicle
various parts of the alimentary canal like stomach, gall bladder,part of the bowel , appendix etc
uterus and ovaries and testes in males though secondary sexual characters may get affected depending on the age of the individual.
Category 2.
pituitary , thyroid etc but these would require supplements.
the list is far from exhaustive.