From the USCCB website:
This is answered in the General Instruction of the Roman Missal (GIRM), number 43:
In the Dioceses of the United States of America, they should kneel beginning after the singing or recitation of the Sanctus (Holy, Holy, Holy) until after the Amen of the Eucharistic Prayer, except when prevented on occasion by ill health, or for reasons of lack of space, of the large number of people present, or for another reasonable cause. However, those who do not kneel ought to make a profound bow when the Priest genuflects after the Consecration. The faithful kneel after the Agnus Dei (Lamb of God) unless the Diocesan Bishop determines otherwise.
Please note this applies to the US only, the rest of the world stands until the Epiclesis and kneels until the Mystery of Faith.
From the QUERY AND REPLY OFFICIAL INTERPRETATIONS OF THE GENERAL INSTRUCTION OF THE ROMAN MISSAL (1975 GIRM):
21. QUERY 3: In some places kneelers have been taken out of the churches. Thus, the people can only stand or sit and this detracts from the reverence and adoration due to the Eucharist.
REPLY: The appointments of a place of worship have some relationship to the customs of the particular locale. For example, in the East there are carpets; in the Roman basilicas, only since modern times, there are usually chairs without kneelers, so as to accommodate large crowds. There is nothing to prevent the faithful from kneeling on the floor to show their adoration, no matter how uncomfortable this may be. In cases where kneeling is not possible (see GIRM no. 21), a deep bow and a respectful bearing are signs of the reverence and adoration to be shown at the time of the consecration and communion: Not 14 (1978) 302-303, no. 4.
Please note the 1975 GIRM has been superseded by the 2003 GIRM, which does not include the Queries from the 1975 GIRM. I believe the same spirit should still apply.