Our house is a combination of old (>100 yrs) and new (~6 yrs) construction with 3 different foundations. There are now many long horizontal cracks, as well as vertical cracks near windows and doors. Should these cracks (thin) be fixed with drywall tape, or is the use of joint compound enough? Thanks for your help!

Not an expert here, but I'd use fiberglass tape over the cracks before any kind of joint compound. The fiberglass tape should provide a better seal against further cracks than just compound alone. If you're mudding anyway, better off using tape too.

You can either V-groove the cracks, i.e. dig the cracks out so they create a v-groove in the wall and patch that, OR you can install tape as kbuchholtz suggested...

I would go with taping as suggested above.

Let us know if need more here...

MARK

I don't quite agree with the fiberglass tape because it is very difficult to work with if you haven't before. Paper tape is thinner and easier to work with.

I wouldn't "V" groove it either since mudd isn't flexible. I would remove anything loose. Sand such that the mud can bond. Then take something like a 2 x 4 about 6" long or so and pound it with a hammer to make a slight depression alomg the crack so the tape fits in the depression in the sheetrock, otherwise you'll have to make a really wide patch. Don't break the paper.

Sheets of sheetrock are not quite flat in. The sheet rock is depressed slightly at the edges, so the joints end up smooth when taped.

You won't see your mistakes till after it's painted. Trust me.

My concern is not the crack yet but the cause and effect. Check the new grades around the house and all down spouts that could cause undermining of footer system. Where are these cracks in relation to the new additions.
I structurally work on old houses well over 100 years old city 1754. Check in the basement of the original house and see what old post are there many times they are old tree posts stacked on some bricks for a base no footer and sinking or moving. Here's what I think the catalyst is. The new addition was tied into the old and it put a different stress "Shear" horizontal cracks on the original house through time. The reason I say this is because where the cracks are.
Window and doors the weakest point for shear and settling. If the cracks are actually in the addition is also settlement but how long did it take for the cracks to show up? I would check out what I said first Or I will Just about Guarantee the "repair won't last long. If this is plaster and lath it's a brittle wall. Been there before

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You should first fasten the drywall with coarse thread drywall screws
In the plaster areas pre-drill with a counter sink bit so you do not crack the plaster
If you use mesh tape you need to use ez sand drywall compound that you have to mix by hand or it will crack
I prefer paper tape with the ez sand
Get r done