All through Great Lent on Friday evenings and of course during the Dormition Fast! It is my wife's favorite. I love it too, but for me, the Presanctified Liturgies on Wednesdays in Great Lent are my favorite. I haven't missed being in the altar or at the Psaltis' stand for one in years (health permitting!).
I posted the Akathist Hymn to this forum, during Great Lent. It is truly beautiful to read; I can only imagine how it must sound when chanted.
In our parish, Friday evenings during Great Lent, we have Adoration of the Cross, when we pray to the 5 wounds of Christ. It concludes with a truly moving chant "O My Son", that usually movess all of the women to tears.