Let's say you have some detailed moulding around several interior doors and you want to strip the paint off with the least amount of labor (time-wise)? How would you go about it? Heat gun, chemicals, removing the trim and reinstalling, etc are all options.
The least time route would definitely be the "remove the trim and replace with fresh" route.
However, this would depend on you being able to get a suitable replacement.
Heat gun is quite quick, but you have to be careful of a) the chemicals released when heating the paint and b) not scorching the wood. Heat guns shouldn't really be used where you've got lead based paint.
Chemicals will be useful where you've got delicate/intricate mouldings but will probably take the longest as you might need several applications if you've got lots of layers of paint.
You will definitely need to sand the mouldings if you use a heat gun, you may have to if you use chemicals. This might not be practicable for delicate/intricate mouldings.
Getting someone else to do it is always the least labor-intensive: if you have a paint stripping service nearby, ask them about doing it. They'll have access to stronger chemicals than you will, and they'll also have the physical setup for taking care of fumes and toxic waste. The service that I used dunks the pieces in a bath of heated solvent which dissolves the paint: no scraping, so no potential for damage to any intricate detailing.
I had a door done a while back; IIRC, they charge by surface area of the piece being treated and it was around US$100 for that (80"Hx30"Wx1.5"D) door. When I got it back, I just had to sand lightly to get the surface back to a milled condition.
This really depends on the age and type of paint, number of layers, and how intricate the wood is. I'd test one or all of the methods on a small area to see what works best.
By far, taking the wood off the wall, stripping it and putting it back is faster and safer. It is much easier to scrap it once its not attached to the wall. Then it is a lot easier to use chemicals.
Heat works very well, but be very careful to test it as you go and not to burn it. As soon as it starts to bubble, scrap it. In my experience, heat has not been useful when there is new latex paint over old paint; it just made the top layer sticky and harder to get off. I usually try to scrap as much off as I can first before using heat. Latex paint sometimes peels off in nice long strips. I've used heat on lead paint before, but wearing a respirator mask and with good ventilation in the room. If you take the woodwork off, this is less of an issue as you can do it in your garage or something.
A heat gun and a sharp triangular scrapper works very well on old mill work and corners. You can also get quartz heaters that can heat a large section of the trim at once and are very effective (but expensive).
A good sharp putty knife works well on latex paints and flat surfaces. You can get good, cheap scrappers of all shapes at flea markets and sharpen them up to snuff. Often the challenge is hitting the paint at the right angle, so try different scrapers if you find that what you are doing isn't working.
If you go with chemicals, wire brushes work really well. My neighbor told me that acetone works well for removing excess sludge that gets stuck in woodwork, but I haven't tried this yet. I try to avoid chemicals as I always seem to spend more time trying to get rid of the sludge than I would just scrapping paint!
Good luck. Restoring wood work is such a pain and there is really no "easy" way to do it. The results can be worth the pain though!