Haha despite the name of the game - I have never paricularly liked the X-Wing. Only got into the game when they announced the Mist Hunter and Punishing One.
Of the stuff I owned and never played are:
There are very few ships I don't have yet:
IG-2000
M-3A Interceptor (Scyck)
Kihraxz Fighter
I'm super excited about the Heroes of the Resistance and Upsilon-class Shuttle. I cannot wait! I am having a blast with the First Order, especially the TIE/sf -- so glad I got two of those! Can't wait to run an epic squad with only First Order ships!
I'm still on the fence about the Rogue One ships, and Sabine's TIE, but I am DEFINITELY skipping the Quadjumper. There's just no away I'll ever play it.
Interesting that now that it's "nerfed," I may pick up a Jumpmaster because I like the design, not because of its meta value. And that really goes for the way my X-Wing aesthetic goes. I have bought mostly what I liked design wise.
I started playing this past June, so I mostly went with newer ships and liked what I saw with Scum, so I'm predominantly in S&V. Looking back, I'd be interested in the Falcon, but lo and behold a new version is coming out. Here are other older models I am fine with not buying:
Z-95 Headhunter (although with two Scum versions already, it may be worth picking a Rebel version up, ditto on Y-Wing)
T-65
T-70 (HotR will do)
All large & epics
A-Wing
E-Wing
B-Wing
K-Wing
U-Wing (on fence till we see more spoilers)
TIEs
Large and Epic (may consider the new shuttle, a Firespray if revised version emerges)
Punisher
Advanced Prototype
Scyk (still on the fence but leaning toward one now that it's Title has been enhanced)
YV-666
GA-1 Starfighter
Well... It WAS the Scyk.
yep, 2 on order...
Some of us were winning tournaments with the Scyk before it became fashionable, dammit
yep, 2 on order...Well... It WAS the Scyk.
Some of us were winning tournaments with the Scyk before it became fashionable, dammit
Exactly Scyks have always been cool... I don't know what +1 Hull is going to do for me. As most games my Scyks were the last things standing.
None
I quit buying at wave eight, and then started going to a monthly xwing night, and then got excited and bought everything but khirax fighter. Epic is fun as well.
My list is as follows:
TIE Advanced
YV-666
YT-2400
Decimator
Ghost
Jumpmaster
Shadow Caster
Protectorate
IG-2000
I've bought the Falcon, Shuttle, and Firespray; But sold the Falcon immediately as i only wanted the cards. Havent offloaded the Firespray because nobody wants one. The shuttle was a purchase for HotAC and is the stand-in for all large ships.
I hate big ships. I think they're boring to fly. I'll buy HotR but i'm still not flying the Falcon. Only buying it for T-70 goodies.
I'm okay not buying:
Jumpmasters
Mist Hunters
Shadow Casters
TIE Punishers
Quadjumpers
Sabine TIEs
Multiples of large ships
Multiple epics
More mats
Otherwise, I either have at least one of everything, or I plan to add one in the near future. I'm still a bit on the fence about the Hound's Tooth, as I'm not a big scum player. The Protectorate will be mine, though, as it fits the Mandalorian niche of the scum faction... (Yes, I'm happy that the recent FAQ gave a bit of a boost to the Scyk for similar reasons, not that I didn't enjoy my Scyks before the fix...)
...who is okay with not getting all of the expansions and which ones?
What's your list?
I'll probably never buy these two either. Don't like the looks of'em and not my style of flying. Already trading for cards in those packs so I don't need the ships themselves.
...
Decimator
I don't plan on getting the Imp Assault Carrier.... unless I win the Lottery, then I'll buy 3. 
I still haven't picked up the TIE/fo, TIE AdvPrototype, TIE/sf, Imp.Vets, ARC, T-70... but I will someday.
I own at least one copy of every ship EXCEPT TFA ones. Thematically, I don't really like them that much (might change my mind!)