I've got a few that would fall under that category to me...most are rare, some aren't. I've found comems, a 1996-W dime, barbers and seated (from some denominations), and even a couple ancient Roman coins. In general, these are the ones from the Seated Liberty period forward that I have either never found or am close to finishing a set from circulation. The one odd coin in the list is the large cent as it would likely only be found searching a different denomination...likely mixed in with half dollars.
CENTS:
* A large cent...any will do
* A flying eagle cent...any will do
* The 12 remaining wheat cents I have yet to find in circulation (in order from highest to lowest mintage):
1913-D, 1932, 1922-D, 1910-S, 1915-S, 1926-S, 1912-S, 1911-S, 1909-S, 1914-D, 1931-S, 1909-S VDB
NICKELS:
* A Shield nickel...any will do
DIMES:
* The 2 remaining silver Roosevelt dimes I have yet to find to complete the set from circulation: 1949-S, 1955
QUARTERS:
* A Seated Liberty Quarter...any will do
* A Barber Quarter...any will do
* A Standing Liberty Quarter...any will do
HALF DOLLARS:
* A Seated Liberty Half Dollar...any will do
* The 2 remaining Franklin Half Dollars I have yet to find to complete the set from circulation: 1955, 1958
There are many other coins on my wish/need list as well as many with a lot more value, but these would be the most desired purely to say I found an example of or that I found the complete set.