Skippable

I don't skip any of the regions for any of my playthroughs.

Only noobs skip!

My Order

Hinterlands: Do all of the quests Mother Gisselle mentions about the refugees there and interact with the cult, as well as get both "helpers" there. I always complete that ring quest too, the one where the elven widow is super bitter.

Go to Val Royueax, gather/interact with the 3 extra companions (viv, sera, IB) Which brings me to the Storm Coast. Where I deal with the Cult and gather some warden stuff for Blackwall.

Side with Mages/Templars

Put off closing the rift, as the Advisors say whoever I allied/conscripted is making their way to Haven. So I go to the Fallow Mire to save our soldiers there.

Then, as the "mages/Templars" should have "arrived" by now, we close the rift and go to Skyhold.

For the most part, I open Crestwood at this point to talk to Hawke's contact to do Adamant First. I've done the Winter Palace first twice now, but it just feels like that's not really the order you're supposed to do it in. Unless Alistair/Loghain is the contact and they fathered Morrigan's child, you're missing nothing in going to Adamant first. So anyway, Crestwood. I close the rift under the lake to stop the undead problem and get me a Mayor to judge. That's all I do here. This also, incidentally, get's Mother Giselle to stop complaining that there is "undead rising" there.

Then I go to Western Approach. Here I do so some stuff. I was fond of making IB's day by hunting the dragon and the giant my last completionist PT, but if my inky isn't best buds with IB or lacks an interest in doing the million fetch quests for Mr Professor to be able to get the Dragon to show...we move on. I often skip the Still Ruins. colfoley takes that one keep because he likes to imagine it a staging ground for attacking adamant. I think I also take it just because. Then off to see Erimond make a mockery of the Wardens, back to Skyhold, make decisions about armor and who's going.

Adamant

I think at this point, I find myself opening places just to get Companion Personal Quests done then skip all the rest of the map.

If I'm Dalish, I go to the Exalted Plains, and I make sure to do as much of the "Grace of the Dalish" I can stand and then leave. Otherwise, SKIP

If I'm Dalish, I also go to the Emerald Graves to do Knights Tomb. Sometimes I can be bothered to do the thing with Fairbanks. Otherwise, SKIP

I go to Emprise Du Lion to free all the slaves and to get to judge the Madame. This gets Mother Giselle to finally report the whole world is okay.

Skip Oasis. Skip Hissing Wastes. Clear my War Table. Round of the Companions. Make Armor.

Go to the Winter Palace.

Clear my War Table again. Play Pick the Divine, finish up personal quests I care about while I ignore the Witch in the Garden Round of the Companions and make some armor.

Arbor Wilds

Clear the War Table. Round of the companions. Make new armor.

End the game.

I've only done Descent and Jaws once. I save them for my best Inky's since to keep them uber fresh. next time I play descent will be with a dwarf. Next time I play Jaws will be with an elf.

To hell with that 3D labyrinth that is the Forbidden Oasis. I only go there one time per year.

I didn't want to do the Forbidden Oasis the first game when I discovered how the occulara are made. Then some of the shards seemed almost impossible to get to so I was left with the final part to do anyway because I didn't have enough shards. However, on completing the game I discovered in the Keep that the Forbidden Oasis is one of the side-quests that is actually recorded. So second run I made a point of getting all the shards, only to find the final battle and reward for reaching the end underwhelming. It had no bearing on the outcome of the game and I really don't see why the fact you completed it needed to be recorded in the Keep. May be I will be proved wrong next game and there will be some bonus to having done so.

First run I decided the keep the Hissing Wastes to complete after I had defeated Corypheus as it gave me something to do post victory. So long as I didn't mind doing it without Solas, in some ways it made sense to do it later. It had no bearing on the main plot and the dwarf history was worth completing the area for. Even so, it did seem odd reading codices that were communications of the Venatori that were clearly meant to be part of the main story. I did it within the game on my second run but went there just to visit the store keeper and collect certain resources on subsequent runs because it did seem to take an eternity to get around it.

I also left most of the dragons until post Corypheus on my first run. However, my second run was the one where I had resolved to do everything with the Inquisitor before facing Corypheus and as a result he was ridiculously easy to defeat. So I think whether or not you do all the areas as part of the main story depends on how challenging you want the final battle with Corypheus to be.

At least I'm not the only one. I find them an entertaining diversion. The first time in the Forbidden Oasis was a bit frustrating as I tried to figure out paths to all the shards, but after that I haven't minded at all and kind of like all the running and jumping. It helps that, because there aren't that many enemies around, you can do all of that in relative peace.

I unlock all areas but i dont do everything in the areas, what i dont do in one playthrough i'll do in the next, both DLC areas i nigh always do

I went to Forbidden Oasis only in my first playthrough, then I forgot about that place forever.

Depends on the mood. In many playthroughs I've skipped the Oasis - because it's a pain in the podex to gather all those shards to unlock the temple but in the last couple times I went there to close the rifts and occupy the place. The Hissing Wastes is beautiful area even it it's too large and too empty. Plus there is the dwarven artifacts you can unearth there in the tomb of ... that paragon whose name escapes me. And closing rifts of course. That's my job after all.

Other than that I would skip Exalted plains since it's such a drag to go through the fortifications infested with hordes of undead. But then there's the Ring of Doubt there, so is the map to the ruins of Dirthamen; and the personal quest of Vivienne is played out there too. So I suck it up and do it!

I only bothered with the Forbidden Oasis once and never again. Fuck that place. 

I haven't skipped any areas yet; in my next playthrough I will try to skip Hissing Wastes because OH. MY. GOD.

Can't tell you how pissed I was when I realized just how massive that map was in my first play through, and worse that it was filled with filler fetch quests.

Never again. That map alone keeps me from playing DA:I a third time.

Also, I hate open worlds. BECAUSE DID I MENTION FETCH QUESTS

I assume it's recorded because it's going to be relevant in the next game. Possibly more so than it was in this one. It's an elven temple, and the text on the walls seems to reference what Solas did. So we might see it again, and Solas might even need to use the place himself.

For myself, I can't say I ever skipped this area entirely, but I've decided not to bother gathering all the shards on my two PC playthroughs, partially because of the underwhelming reward and partially because I want to see what difference it makes in DA4 if I don't. (My three PS3 characters all finished that one.) If I ever get started on that second Vashoth I have planned, though, I think I might have to send her in there. I'm not sure how the Arishok's personal Vitaar wound up in there, but however that works, it means if you want a purple item for your Qunari PC's head slot...