9. Taking a Sefer Torah out of the Shul not for the sake of Kerias Hatorah:[1]

It is permitted to remove a Sefer Torah from the Shul for the sake of its honor and respect. This includes the following cases:

Hachnasas Sefer Torah:[2] It is permitted to remove an old Sefer Torah from the Aron for the sake of dancing with it by a Hachnasas Sefer Torah. It may be danced with even in the streets together with the procession of the new Torah.  

In honor of a King or president: Some Poskim[3] rule that it is permitted to remove a Sefer Torah from, the Aron for the sake of greeting a dignitary, such as the president or king.

Hakafos for Simchas Torah: See previous Halacha in Q&A!

For the sake of editing it:[4] It is permitted to have a Sefer Torah brought to the home of a Sofer for the sake of checking it or editing it.

[1] Piskeiy Teshuvos 135:28

[2] Michtam Ledavid 15; Ikarei Hadaat 8:28; Beis Shearim 49; Piskeiy Teshuvos 135:28

Other opinions: Some Poskim rule that it is forbidden to remove an old Sefer Torah from the Aron even for the sake of dancing with it by a Hachnasas Sefer Torah. [Birkeiy Yosef 135:13 that the Sages protested against this being done] Other Poskim rule one may remove the Sefer Torah from the Aron and dance with it inside the Shul, but may not remove it from the actual Shul to outside. [Shaareiy Efraim 9:46]

[3] Pischeiy teshuvah Y.D.282; Chinuch 179

[4] Ikareiy Hadaat 8:28 in name of Pachad Yitzchak and Shivcheiy Todah; Mishnas Avraham 40:5; Kaf Hachaim 135:79; Piskeiy Teshuvos 135:28