Flydog,
Where climb gradients are given, they are established to provide minimum terrain or obstacle separation. If you can maintain your own terrain or obstacle separation, you needn't comply, except when cleared for a specific departure proceedure. In such a case, the clearance is binding, along with all the applicable restrictions in the DP.
If operating under FAR 135, you are required to meet specific obstacle clearance requirements. 135.379(d) provides that within the airport boundaries you must achieve a minimum vertical separation from obstacles of 35', and a minimum horizontal separation of 200'. Once outside the airport boundaries, the minimum horizontal separation is 300'.
Your Opspecs may have specific individual limitations.
You should always consider each takeoff based on your ability to achieve the minimum climb gradient with an engine out, based on your second segment climb capability. If the issue is weather or not you can meet the minimum climb gradient with all engines running, then you need to look seriously at the takeoff and make some changes. Meeting the minimum climb gradient with all engines running shouldn't be an issue; meeting the minimum climb gradient with an engine out shouldn't be an issue, either.
If you are unable to comply with the minimum climb gradient, you should notify ATC. They are expecting the minimum, and may have specific requirements for you. You may be expected to maintain your own terrain separation, or be asked if you can maintain your own terrain separation, until a specific altitude. In congested areas, it is especially important to notify ATC if you believe you won't make the necessary gradient, as ATC may be predicating your control and separation on your ability to make the minimum. This may require special handling, and timely notice makes the job easier for everyone.
Bear in mind that the inability to meet published terrain separation criteria may be grounds for enforcement under FAR 91.13, or 91.103. There is not a specific FAR which states you must meet the climb criteria, unless it is issued as a clearance (cleared via the tambo six departure, climb and maintain...). In such a case, you must comply with the clearance, as outlined in 91.123(a). However, accepting routing which exceeds the performance capabilities of the airplane can always be grounds for enforcement, even if a clearance is not violated, or required.
Note that the criteria in TERPS, which is used to establish the published minimum climb gradient, doesn't take into account weather engines are operating or not It's simply the minimum required to clear obstacles. It is up to the operator to determine if the aircraft can do it with an engine out. Takeoff weight is limited by this ability. Operators must either show compliance with the TERPS criteria with an engine out, or show alternate routing. See FAA Order 8400.10, Volume 4, Paragraph 927(e)(2).
It's also important to note that FAR 135.379(d)(2) specifies a net flight path, which is less than the climb gradient achievable as shown in the aircraft flightmanual performance section. Net flight path is a concept that reduces the demonstrated climb gradient by a specific percentage, to ensure a safety margin. Therefore, one must be able to do more than just the minimum climb gradient to meet minimum takeoff standards.
135.379(d) does not limit the departure to climb gradient, but limits the departure by weight. This paragraph prevents an aircraft from departing at a weight greater than what would allow that aircraft to meet obstacle clearance requirements. The implication is that you need not meet the gradient, but you must clear the obstacles. If you cannot mee the gradient, you must still be able to ensure that the fligth meets the minimum obstacle clearance requirements for the departure path in use. This may, or may not, require a specific clearance (depending on the location, and the conditions).