As I write this, the average orbital altitude has dropped over 8 km already since the ion engine shut down on October 21st. Yesterday afternoon (25 October) the average orbital altitude had already dropped below 220 km altitude, with the perigee now below 217 km (see first diagram above).
GOCE is currently losing altitude at a rate near 2 km per day. That rate will notably increase over the coming days, as GOCE will drop faster and faster.
It is too early yet to provide meaningful estimates of the re-entry date. My current prognosis (for which I used Alan Pickup's SatAna and SatEvo software) suggests a re-entry in the second week of November, but note that this date will probably shift to an earlier date over the coming week.
Currently, the satellite is still maintaining an attitude (orientation) that is optimizing for low drag. It does so using magnetic torques. At some point close to re-entry, that system will probably fail and GOCE will then lose attitude control. As it does so, drag will increase, which will seriously influence the re-entry date, shifting it to an earlier time. Meanwhile, the sun has been quite active the last few days, which speeds up the decay as well as the density of the Earth's outer atmosphere changes under the influence of solar activity. My very preliminary prognosis was made with an average forecast F10.7 cm solar flux of Fx=135 for the coming 20 days, but unexpected solar outbursts might alter the true picture.
I expect that several sources will start to provide re-entry estimates in the days before re-entry. The chief authoritive sources will be ESA itself, and the TIP-messages by USSTRATCOM on their Space-Track portal (needs an account to access). I expect that several independent analysts will provide re-entry estimates as well. The Aerospace Corporation provides re-entry estimates based on their own re-entry models, but is usually lagging behind. Their predictions sometimes strongly differ (up to several hours) from the final re-entry times and locations determined by USSTRATCOM (which I consider to be a more reliable and authoritive source).
(note: in the first diagram above, the values for perigee and apogee show some short-term fluctuation during the first 2-3 days after engine cut-off. These fluctuations are the result of errors in the orbit determinations, which easily occur (and are inevitable) when the data-arc used is still short and fitting error margins are hence wide. As the observational arc grows, the orbital determinations become more stable, which is indeed what we see over the last two days.
The apogee and perigee altitudes in the first diagram have been calculated from the values for Mean Motion and eccentricity using a fixed Earth radius of 6378 km, ignoring Earth's oblateness. Orbital elements are from USSTRATCOM (needs an account to access) with a secondary source (open access) here).
Note 31 Oct 2013: a new update here.