I think the best way is to manually allocate citizens in your city to work for things that generate more gold / production / food / culture over science.
For example, if you leave your citizen allocation for the "governor" (the AI), it will surely prefer a "2 production / 5 science" hex to a "2 production / 1 gold" hex, even though the latter is better for you. Remember that for manual allocation you must first open the citizen allocation menu in the city screen, and also remember you can allocate citizens in buildings, for the buildings that allow it (called specialists).
You can also leave the allocation to the AI and only direct his effort by choosing something to focus on, via the radio buttons in the manual allocation menu. Those work better when you want something specific, though, not when you want to avoid something specific.
Finally, remember that even after you have researched everything, you can continually research the repeatable "future tech" technology for extra points. It gets harder and harder to complete it every time you repeat it, so you can never have too much science if you go this route.
By the way, if you have built any academies you can now override the hex containing them with some other improvement / great person structure, that can also help if you want to redirect your efforts elsewhere.
EDIT the newest version of civ5 allows you to sell buildings - which is perfect for this case! Just sell all your research labs, universities, libraries etc. - sell all buildings that only give you science. Since you can sell only one building per city per turn, I recommend you start by selling the buildings with the highest maintenance cost.
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
Ways to speed up your teching:
Establish trade routes with him for science income, pass applicable things in the UN like Scholars in residence and arts funding. Use faith to purchase great scientists and enter the rationalism tree/take science policies like workers faculties or the one that makes speis better at stealing techs. You probably can improve your city micro and tech pathing as well.
Ways to slow down their teching:
Go to war with them, hire someone to go to war with them, embargo them, tamper with their religion if they have one,
That said, at high enough difficulties Korea and Babylon are going to be strong techers, and without a tech focused civ you will have trouble keeping up with them. It sounds like you are going for either a culture or diplo victory, since its peaceful and not science. In that case, you need to concentrate either on preparing a bunch of great scientists for bulbing to internet, or simply allow yourself to fall behind in tech. Being behind in tech is least important to a diplo strategy.