One way to make sure your gutter doesn't fall off the house is to install fascia hanger brackets. Installation is simple: Just hook the bracket under the front lip of the gutter, and then screw the other side of the bracket to the fascia. Leave the old spikes in place—a spike head looks better than a hole in the gutter.
If your shingles overhang your fascia by a few inches or you have steel roofing, buy the brackets with the screws built in (the type shown here). They cost more, but the head of the screw remains a couple of inches away from the fascia, making them a lot easier to install.
Water Gets Behind the Gutter
A gutter apron is a bent piece of flashing that tucks up under the shingles and over the gutter. Home centers sell a gutter apron in 10-ft. sections. You may have to temporarily remove your hangers as you go, or you can notch out the apron around them. Once the apron's in place, fasten it with sheet metal screws.
If there's a drip edge installed where the fascia meets your shingles and the gutter is hung below the drip edge, get some roll flashing and tuck it up under the drip edge and over the top of the gutter. Home centers sell rolls of 6-in. x 10-ft. aluminum flashing. Use tin snips to cut the gutter apron flashing roll in two 3-in. strips. If your gutters are steel, buy steel roll flashing, because galvanized steel corrodes aluminum.