For me the whole point of playing Civ is to enjoy myself and unwind for an hour or two after the kids are in bed. I do not want to get stressed by a game. So I routinely do the following:
1. Regenerate the map if the starting position is hopeless.
2. If not entirely hopeless, I will tweak terrain features, such as changing mountains to hills and moving a resource or two or adding a hill or two.
3. I allow myself unlimited WTH (What the F***) reloads. This is the stereotypical "a spearman killed my tank" sort of thing. I hate that crap, and totally wish that Civ had an option like the "low luck dice" in some Axis&Allies variants.
4. I allow myself about 10 BIFLI (Because I Feel Like It) reloads per game. This is for times like when I am hoping to pop a Great Prophet, but get a stupid Great Bard instead.
5. I allow myself about 10 WBM (Way Back Machine) reloads per game. This is for when I spend 30 turns building a Wonder, only to get it sniped out from underneath me by another civ when I had one turn left on the build. In these cases, I go back to the turn that I first initiated the project, and see if I can win the race by putting my city in "total production at all costs" mode.
6. I allow changes to the map if I make a sacrifice of some sort. Such as:
a. I can expend a Great Prophet to change a coast plot into a marsh. I call this a "Parting of the red seas" action.
b. A Great Prophet can also change mineral resource into a different mineral resource, but the unit must similarly be deleted.
c. A Great Prophet may change a volcano into a hill. The opens up new passages in erebus maps sometimes, and I absolutely love it!
d. A Great Merchant can move any resource that is plausably moveable. Most food resources and some luxury ones fit this category. I call this the "Opening New Markets" action. But the Great Merchant must travel to the plot that contains the resource, "pick it up," and then move to where I want to put it. The target plot must be appopriate (no dye in tundra), and then the unit is deleted after the resource is relocated. This usually means that the Great Merchant must be escorted, and makes for some fun adventures!
e. A Great Engineer can change a mountain into a hill, a marsh into grass, floodplains into grass, clear all jungle from a city working radius, or slightly alter the course of a river. This expends the unit, and I call it the "Great Public Works" action.
Anyway, that is how I cheat. Again, my whole reason for playing Civ is to have fun and I will happily cheat my way around buzz killers when needed. I respect the fact that other people play differently and have differing levels of tolerance for cheating. We all play differently, but we all play Civ!