We have created a number of volumes at the MNI, one that defines the MNI stereotaxic space (MNI305) and a few others that are in this space (see the viewer for example images). Here is a bit of history:
The MNI stereotaxic space was first defined by an average of 250 T1-weighted volumes, brought in to stereotaxic space manually using the technique of Evans et al and the resulting model of 250 volumes was described first in an abstract . This model was never made public.
This initial target was then used to build an average of 305 T1-weighted volumes using an automatic cross-correlation method described in a paper by Collins et al  where the model was described in an abstract . This is the model that we use to define the MNI stereotaxic space and is known as the MNI305 average. The model is available from our site as the mni_autoreg_model (at bottom left of page). It was also included in SPM99 and was an option in SPM97.
This model has been improved within the context of the ICBM project . 152 T1, T2 and PD volumes were used to create 3 averages (one for each image type) that are defined in the same space as the MNI305. These models are known as the ICBM152_T1, ICBM152_T2 and ICBM152_PD averages. The advantage of these data include better contrast and better definition of the top of the brain and the bottom of the cerebellum. These will be made publicly available.
In another project, Colin Holmes (who was then a post-doc at the MNI) scanned himself a number of times. We registered the 27 T1-weighted data volumes together to create the Colin27 average. This data has very high S/N resulting in beautiful structure definition. The procedure used to create this volume was described in .
The Colin27 average was used as the basis to create a numerical phantom  that was combined combined with an MRI simulator designed by Remi Kwan  in order to simulate realistic MRI data in a controlled fashion. These simulations form the basis of BrainWeb where we created a large database of simulated images varying slice thickness, noise levels and intensity nonuniformity . It is important to note that the BrainWeb DB is in MNI stereotaxic space, it does not define it.