Many, many, many.... but one that I want to remedy soon is a Seated Liberty half dollar. I don't know why, but the halves are much for attractive to me than the other denominations.
I've never owned many of the early gold coins, but would love to eventually complete a type set at some point (I'll forgo the Stella for Matt). I would also love to put a flowing hair dollar in my collection. I even had the means to pick up a nice 1795 three leaves last year, but decided to wait on the three leaves that was coming up a few lots later. I should have bought the first one, the second one went crazy on price for some reason. It was nicer looking than the first (both XF-45), but the second nearly doubled the price of the first. Luckily a dealer friend of mine gave me the don't bid look and saved me from overpaying for it. It may be the highest on my want list, but that will probably change tomorrow.
A $3 gold piece is next on the want list for me, I've never even held one yet! Determined to not get a common date either.
There are multiple varieties of the Henning nickels - I collect them with my "black cabinet" stuff. There is a variety of the 1944 that doesn't have the divot in the R.
My list I've never owned Small eagle half Chain cent Liberty cap half cent Small eagle quarter Gobrecht dollar 1792 Half disme Any pre 1835 gold Draped bust and flowing hair dime $3 gold. Really! Just haven't seen one I wanted Type 1 liberty double eagle All are coins I want I may never be able to afford some of them but who knows as to the often mentioned trade dollars those I'm trying to complete the whole set of less the 84 and 85. When that's done maybe then I'll own a few of the tougher ones on my list or maybe not! As to trade dollars up til this last week I never had a cc one
There are quite a few designs that I have never owned. But, the short list that comes right to mind is I have never owned a US half cent, Bust Dollar, Seated Liberty Dollar or Trade Dollar. My experience in gold is pretty limited too...I have only ever owned a St. Gaudens Double Eagle and a $1 Type 2 Gold Indian.
Wow, there are so, so many US coins. Partly for that reason, I'm attracted to Carson City mintage - it's not outrageously impossible to own one of every type they minted there for a "reasonable" expense. Hah! Duk
I currently own 2 of the $20 liberty from there, the 1893 I own is one of the lowest mintage coins from the USA that I own - something like 19k minted - and the things do trade at a markup over spot of course but not outrageously priced like say a cent or nickel would be at that mintage level.