Byron's "When We Two Parted" has a definite anapestic rhythm, despite the fact that most lines begin with two-syllable feet and others end with unusual feet such as, "I greet thee," which scans as * / /. Some people would call it simply accentual dimeter, but on the whole, it's a good example of anapestic dimeter:

                          *   / |  *    *   /
                         In secret we met--
                              In silence I grieve,
                            That thy heart could forget,  [perfect anapestic dimeter: * * / | * * /]
                              Thy spirit deceive
                            If I should meet thee
                              After long years,
                            How should I greet thee?--
                              With silence and tears.

Here is William Blake's "The Echoing Green," which is dominantly anapestic dimeter. Of course, there are some lines that do not begin with perfect anapests, and the feminine rhymes add hypermetric syllables to some lines:

Till the little ones, weary,
No more can be merry;
The sun does descend,
And our sports have an end.
Round the laps of their mothers
Many sisters and brothers,
Like birds in their nest,
Are ready for rest,
And sport no more seen
On the darkening Green.
 

This is also basically anapestic dimeter:

            THE sailorman's child
            And the girl of the witch--
            They can't be defiled
            By touching pitch.

            The sailorman's son
            Had a ship for a nursery;
            The other one
            Was baptised by sorcery.

            Although he's shipped
            To the Persian Gulf, her
            Body's been dipped
            In burning sulphur.
                        --Elinor Wylie