While both the intensity and covariance quantities presented in the Planck all-sky maps are, by definition, positive, there are situations in which you will see negative values.

o In regards to the Planck intensity maps:

To begin with, the Planck all sky intensity maps do not have the Cosmic Microwave Background [CMB] subtracted. The CMB subtracted maps can be found together with the component separated CMB maps, for example at:
http://irsa.ipac.caltech.edu/data/Planck/release_1/all-sky-maps/previews/COM_CompMap_CMB-smica_2048_R1.20/index.html

However, negative values in intensity (but not covariance) can occur because of noise.

o In regards to the Planck covariance maps:

Covariance values should not be negative. but the negative values in the covariance are HEALPix bad values, i.e. -1.63750E+30.

That being said, the covariance in some of the maps are plotted in units of log(II_COV) which could be negative even if the number is positive.

Here is an example in IDL  based on the 100 GHz (R1.1) map in Data Release 1 called HFI_SkyMap_100_2048_R1.10_nominal.fits:
HIDL> gb = where(m.ii_cov ne !healpix.bad_value)
HIDL> print, minmax((m.ii_cov)[gb]) ; this is only the valid pixels
% Compiled module: MINMAX.
1.20344e-11 1.38910e-07
HIDL> print ,minmax(m.ii_cov) ; this is all pixels including the pixels with no coverage which have the healpix bad value
-1.63750e+30 1.38910e-07