As you might have guessed, this maintenance was not done on our gutters for many years, and the attempts to patch and repair them have not done them any favors. As a result, we've ended up with rotted eaves and water in the basement. We decided to tackle the porch gutters ourselves and see if we're up for doing the work on the rest of the house before we invest in scaffolds and other equipment.
Yesterday I removed all the fascia boards and soffits to see the extent of the damage and formulate a plan for repair. Luckily, most of the water damage is on the trim boards and not on the structure itself. Two of the lookouts (the boards that support the gutters) will have to be replaced, as well as all of the gutters. But the porch rafters and beams look fine, so rebuilding ought to be simple.
Just for kicks, here's a picture of some of the previous "repairs" to the metal gutter liner. In case you were wondering, roofing tar is not an acceptable long-term solution for this kind of work!