A few minutes contemplation suggests that many shows have this feature. However I think there are at least two types of shows that fit your general request.
One type places the willingness for self-sacrifice at the core of the story like
Moribito does. I'd add
Kurozuka,
Noein,
Real Drive, and perhaps
Kure-nai and
Ergo Proxy to this list. The pilots in
Yomigaeru Sora: Rescue Wings must contemplate sacrificing themselves to save others on every mission.
In other cases self-sacrifice represents just one event in a larger plot as in
Twelve Kingdoms,
Kemono no Sou-ja Erin,
Toshokan Sensou,
Monster,
Saiunkoku Monogatari,
Mouryou no Hako, or
Mononoke Hime.
Tokyo Magnitude 8.0 and
PlanetES might also qualify here. Even
Dennou Coil touches on these issues at a number of moments.
The Apothecary in
Mononoke might be willing to sacrifice himself to defeat the demons he faces, but I think he believes he's so superior to his supernatural and human enemies that he's invincible. The same probably applies to Twenty Faces in
Nijuu Mensou no Musume.
In his most angsty moments, Harima might consider sacrificing his life for Tenma-chan in
School Rumble, as might Hanai for Yakumo, and both might be stupid enough to do so. (OK, I'll admit I might offer to sacrifice myself for Yakumo, too.)