Please note that this question is asking whether antique money is still legal tender today, and not about what you could buy with it today. Remember the 20 year rule.

Short Answer:

Yes, still legal tender

Coins of 1866 - 1c, 3c, 5c, 10c and 25c

Fun Numismatic History:

In 1862 a new class of money, legal tender notes were issued and these are pretty much the notes we use today with the exception that they state they are redeemable for $X amount of gold/silver. Issued in denominations $5, $10, $20, $50, $100, $500 and $1000. These notes replaced the short lived demands notes of 1861/2 that were the first nationally issued paper money. The next year 1863 saw the introduction of $1 and $2 notes as coinage was rapidly being taken out of circulation and hoarded.

Mintage of the half cent stopped in 1857 so those were likely out of circulation by the end of the Civil War. This means the penny was the lowest denomination in circulation. Large cents, a one-cent issued with a diameter of 1.125 inches (hard to imagine today especially for a penny, for comparison a quarter is .955 inches) had been out of date for awhile at this point and the second iteration of the small cent (modern size of a penny) would be in the pockets of Americans in 1866. The Indian Head penny had been minted since 1859 in sizable quantities. The Indian Head graced obverse is the predecessor of Lincoln's head while the reverse has seen changes in design before its modern day counterpart.

The two cent piece is an interestingly short lived piece of American numismatic history who likely had its heyday in 1866. Minted from 1864-73 it saw roughly 19.8 million and 13.6 million produced respectively in its first two years with under 10 million minted during the remaining seven. Alongside the two cent piece was the three cent coin who enjoyed a longer period of success. First minted in 1851 it enjoy production through 1889. 1866 is a very interesting time in the three cent coin's history as it was beginning its conversion from a silver composition to a nickel one. 1866 is the last year the the silver three cent coin had a mintage of over 5,000. Conversely that year the nickel three cent had a mintage of over 4.8 million.

The nickel we are familiar with today, at a value of five cents, was first issued in 1866. Almost 14.75 million were minted the first year. I have posted before on the history of the nickel and its three cent predecessor here. By this point in time the ten cent piece, the dime, was rocking its third design. The dime's small value and 90% silver composition are the contributing factors to making it the smallest circulating coin.

The quarter is on its third design and second iteration of this design. Featuring Lady Liberty, like all other silver coins of this period, the quarter had just that in 1866 had the motto, In God We Trust re-added to the reverse after being taken off in 1828. The half dollar also featured the same Seated Liberty and had also just had the motto reintroduced. This is also the same for design for the silver dollar.

Gold coins, although minted in denominations of $1, $3, $5, $10 and $20 were minted for 1866 although they had not been in circulation, and rarely were to begin with, since the outbreak of the Civil War.