1. How do I handle this? do I need to make sure all the wood on the doors, trim, and floor have the same color stain?
You need to look at the house, and see what flows, and what does not and make the change.

2. If so, is it possible to stain the existing woodwork darker without an excessive amount of work ( like sanding it all the way down)?

Gel stain can be used, you will still need to do some sanding to remove the shine so the stain will stick.

3. Is wood trim and moulding considered dated, these days?

Trim is what gives the home character, all depends on what style you want, i.e. Modern, Craftsman, Colonial.

4. Would it be better to go with replacing it all with white composite? (Lots of the woodwork needs repair as the previous children used it as a medium for carving pictures and their names)

If you just want to paint I would try to repair the trim, and see how much time it takes. While replacing trim may be easier you still may have to patch walls, and fill nail holes, etc.. Doing this now to my house, and it is a big chore.

5. The windows are also the same color of wood, would it look strange if they didnt match the trim around them?

No need to replace the windows, even today people buy white vinyl replacement windows to put in with natural wood trim.

2. If so, is it possible to stain the existing woodwork darker without an excessive amount of work ( like sanding it all the way down)?

I took dark kitchen cabinets, painted them a dark yellowish color, stained them with an oil based stain and ran a tool down them to simulate wood grain. Finished with three coats of Polycrilic satin. Son in law is a contractor and thought they were new at first look.
So, sure you can stain them, you just have to seal the stain in.

What hendricus describes is possible, but also takes some work and skill; otherwise it can look crappy. Also, because it is a surface treatment, scraping, scratching, or other damage will be more obvious. In my opinion, there is no easy way to re-stain in place wood that has been stained/sealed -- and have it look decent -- which is what I think is being asked about. The easiest thing to do is remove what you don't like and put in something you do.

"Sanding is a really expensive and laborious way to remove finish. Stripping is much better. "

Nobody strips floors.

It would take massive amounts of stripper and likely more work than running a drum sander back and forth.

Nobody was talking about stripping floors, Brickeye. The discussion is about trim.

I would not worry at all about the window components being wood that is stained while you change the trim out to painted. Whether you repair the trim or replace it has more to do with whether you like its style and whether it is worth the work. For instance, my 1978 ranch had a simple and cheap baseboard molding used as door casings (according to my carpenter, who replaced it for me). I had to have it replaced for two reasons: we put new flooring in and the baseboards were removed, and the old baseboards were not worth the effort to repair and replace, and door casings on the two bifold door closets had broken over the years where it extended past the wall in order to hide the door edges. Cheap trim is not worth the effort. We replaced it with a very simple, but standard quality trim. Now I have to prime and paint the baseboard and door trim.

In my case, my doors remain a very dark stained color (not oak, an indeterminate wood that is invisible under the stain, it may be one of those gel stains done by the previous owner). I am trying it out to see if it will look okay with painted trim. I am not sure of my wall color or trim color yet, so I will not have results to share with you anytime soon, just wanted to chime in and let you know that you are not alone. I would have, however, gone with stain-grade wood if I could have fit it in the budget. I have dark stained oak in the one room where the trim was done by my contractor. I would have been happy to have added a good quality stained oak trim everywhere!

There are several posts on the kitchen forum about gel staining oak cabinets. They turn out very nice. I would consider doing it were I in your shoes.

Here is a link that might be useful: gel staining cabinets

1. How do I handle this? do I need to make sure all the wood on the doors, trim, and floor have the same color stain?
>>This is a matter of personal preference so there's no absolute right answer. Personally I like the doors, door trim, base and crown mold to match. They don't need to match the floor but of course they do need to be complementary.
2. If so, is it possible to stain the existing woodwork darker without an excessive amount of work ( like sanding it all the way down)?
>>Yes it is despite what I've read others claim. Speak to a reputable painter who is skilled at wood finishing. Just as is used on kitchen cabinets, there are stains that can be brushed or sprayed over existing finish once it's properly prepared. As long as you're going darker, it's not necessary to sand all the way to raw wood.
3. Is wood trim and moulding considered dated, these days?
>> Styles come and go. Unless you move every few years, do what you like, not what would appeal to the majority.
4. Would it be better to go with replacing it all with white composite? (Lots of the woodwork needs repair as the previous children used it as a medium for carving pictures and their names)
>> If you're going to paint, damaged areas can be filled, sanded, primed and painted. Just keep in mind that the grain on the old wood might show through in the finished product. Do a test on a piece to determine whether it meets your expectation and consider the cost difference between replacement and refinishing or painting.
5. The windows are also the same color of wood, would it look strange if they didn't match the trim around them?
>> There again it's personal preference. I prefer that they match. There's nothing that says you can't paint the wood.

I read your post and could've sworn you'd moved into my parents' previous home (built in 1996!!) Does the kitchen cabinets have arched raised panel doors, too, and a green marbled laminate countertop?!?!

If trim is in terrible shape, I'd replace it using a style that you like (i.e., craftsman, colonial, etc.) and would paint it.

You could either paint the interior doors or leave them stained. (houzz.com has tons of photos of white trim and stained doors)

You might consider refacing the cabinets (if you don't like the door style) or just painting them. Benjamin Moore supposedly makes a wonderful product for cabinets.

Stacylh- No, it doesnt have arched panel doors, but it does have a hideous green laminate counter top! lol

Thanks everyone for your suggestions. After our inspection we found out we likely need to replace all the windows, anyway, so I guess that solves one issue. If I purchase white windows, then the white trim will like better. IMO.

Personally I would paint all the trim white, put in nice hardwood in a color you like, and either paint the kitchen cabinets white or gel-stain them darker!

I love wood floors but I am not a fan of wood trim everywhere unless it fits the house (log cabin etc).