This isn't a full list of all the coins that are faked, just the ones I believe are the most commonly encountered ones.
Half Cents1793, 1831, 1836 - 1849 except the 1849 large date
Large cents
1793 all types, 1799, 1804, 1815 (all are fake),
Small cents
1856, 1872, 1877, 1908-S 1909-S, 1909-SVDB, 1914-D, 1922-"P", 1931-S, 1943 copper, 1955
DDO, 1972
DDO Two Cent1872 and these are not common.
Three Cent Silver1858, 1861, 1862 (all of these are crude contemporary fakes)
Three Cent NickelNone that I know of.
Nickels
1875 (contemporary fake), 1878, 1880, 1881, 1885, 1912-S, 1913-S Type II, 1918/7-D, 1926-S, 1937-D Three legged
Half Dimes1795, 1802, 1846, 1853 No Arrow, 1853-O no arrow, 1863, 1864, 1865, 1866, 1867, 1868
Dimes
1796, 1822, 1844, 1846, 1853 no arrow, 1860-O, 1863, 1864, 1865, 1866 1867, 1871-CC, 1872-CC, 1873-CC, 1874-CC, 1916-D, 1942/1, 1942/1-D
Twenty Cent1876-CC
Quarters (I don't know these well)
1870-CC, 1871-CC, 1873-CC, 1896-S, 1901-S, 1913-S, 1916 SLQ, 1918/7-S, 1923, 1932-D, 1932-S
Half dollars
1794, 1796, 1797, 1806, many of the dates 1818 - 1836 these are contemporary fakes and are often worth more than the real ones, 1870-CC, 1878-S, 1914, 1915, 1921, 21-D, 21-S
Silver dollars
1795, 1796, 1799, 1804, All
Seated dollars, All
Trade dollars, 1889-CC, 1893-S, 1894, 1895, 1895-O, 1895-S, 1928, 1934-S
Gold coins
I don't know much about the pre-1934 coins. All of the post 1834 coins are at risk especially the Type II gold dollars and the three dollar gold. With the type II dollars and three dollar gold pieces there are probably many more fakes than there are real ones. When ANACS began back in 1972 more than 90% of all of the type II gold dollars and three dollar coins submitted were fake.