Is my landlord responsible after I fell in a hole at the apartment complex I live at while taking my garbage out?

It depends on whether your landlord and/or you knew the hole was there. If your landlord knew it was there beforehand and failed to repair, or guard or warn you against it and it wasn't an open and obvious hazard, then the landlord could be liable.

Yes if he had notice, lack of maintenance etc.

If the hole was open and obvious to casual inspection, then probably not. However, if the hole was covered by tall grass and not readily observable, then it wouldn't hurt to try to make a claim with the landlord's insurance company.

If the landlord had prior notice and failed to cure the problem, or if the landlord made the hole, there will be some responsibility on his part. But you might also have a share of the fault if you didn't watch where you were walking. These are not clear-cut cases.

The answer depends in part upon what notice the owner had of the existence of the hole and an opportunity to fix it. Also depends upon whether you were aware of the hole or should have been aware of it.

Depends upon whether hey had prior knowledge of the hole. Also, if you have no major injuries, your damages is very small.

Your landlord is not automatically responsible. Generally, the person(s) who have garde/custody of the area where you fell would be responsible for the condition of the area. Often times this is the landlord, but it might be someone else and sometimes more than one person might have garde/custody. Garde/custody of the area does not make one automatically responsible but instead places obligation on him, however, other factors to consider would be who/what caused the hole to form, how long the hole was in existence, whether or not there was appropriate warnings, and whether or not you knew/should have know of the hole's existence. This response is a general response and I would recommend that you speak to an attorney if you have more specific questions as each situation is different.