Tedium comes from feelings that you're making a lot of decisions that don't really impact anything. So...
Minimize how many decisions you have to make:
(Of course, try to get rid of the decisions that don't matter, and keep the ones that do.)
- Automate! If you're bored with workers, set them to automate, and make them stop pestering you. There's also an auto-explore.
- Move your units where you really want them to go, not just this turns movement points.
- Fortify or dismiss unit when they're really not helping anymore. They stop asking for orders!
- Set build queue for cities. (thanks @Colen)
- Open the tech tree and tell it to research to something late in the tree. I think with shift or ctrl you can queue up techs as well.
- Puppet Cities - Rather than controlling every city yourself, take over a few, and leave them as puppets. They benefit your civilization, without costing your decision making time.
- City States - For that matter, don't take over city states if you don't have to. They'll help you just fine as they are, with the right convincing.
- Play on faster speeds - This minimizes the extra turns you make decisions for only units, often needlessly.
- Play on a smaller map - Getting places doesn't take a long, and there will be less cities/units overall.
- Play against less opponents - This is best accomplished as a consequence of playing on a smaller map, and the benefits are the same: less decisions to be made.
From my experience, quick games on average are just more fun, because even if the game is bad, its over quickly. Then you start a new game and have a chance to learn from mistakes all the sooner!
In general I agree - in late-game, GP are less useful and I usually trade them in immediately for a quick golden age. However, unless you have absolutely everything, great scientists and great engineers do have some value, and there are use-cases where the rest are useful as well, I've listed them below.
Remember golden ages are always great, even if they are short. +gold, +production and no happiness issues.
Great Scientist: if you already have everything then this is indeed useless, but as long as you don't this is still useful. It's true late-game technologies are usually researched quickly but there are a few wonders in late game and being the first to reach them can be nice; furthermore, being the first to unlock Aluminum or Uranium is good because you can plan your land acquisitions better.
Great Engineer: there are some wonders in the late game, and they are pretty good actually. Other than that, great engineers are useful if you create a new city in the late-game; I usually buy a lot of buildings whenever I do this, but a great engineer can save a lot of money by speeding the most expensive buildings.
Additionally, factories are always useful.
Great Merchant: whether you should use the diplomatic mission or the golden age is not always obvious - see my answer to another question to see my opinion. In general I say a diplomatic mission is usually worth more gold, but a golden age also nets production. Custom houses are not worth it, in my opinion.
Great General: I almost always trade them for a golden age immediately, with one exception - I sometimes build citadels in natural chokes or other appropriate locations. From experience, a single citadel in the right spot, backed by 2-4 units, can stop an army.
Great Artist: the most useful type in the late game! Using the culture bombs allows you to reach practically everywhere. I one time used 3 of them to get to just one Aluminum patch in the middle of an icy area (just took a little time because of the cooldown). They can also be used to steal stuff from civilizations and city-states.
Also, landmarks are always nice in cities that already have a lot of +% culture.
Regarding city states: I usually do use great people from city-states, late-game maintenance costs are high but I think a golden age is always worth more than the time it takes them to get to the nearest border, even if it's a golden age lasting just 3 turns.
EDIT as of the June 2011 patch, great person improvements have been buffed:
- Erecting a great person improvement automatically connects a strategic resource if there's one on the tile
- Each great person improvement has an associated technology which increases the tile yield when researched
- Completing the freedom tree doubles the tile yield
This means using great people for improvements is a more viable option now.
Best Answer
This is a very conditional answer, but if the AI beats you with a Time Victory, what happens is that the option to choose "just one more turn" is disabled. [Source 1, Source 2]
I haven't been able to find out what the AI does in the case of other victories though. There's a forum thread with the same question, but unfortunately it doesn't get very far:
How does the AI behave after somebody has won?