What happens when two polarized lights of the same wavelength interfere at 90 degrees with each other?

Wether you get destructive interference or constructive will depend on the position. What you get is something like in the image. Where the diagonal lines indicate maxima where constructive interference occurs while between them there is destructive interference.

The interference pattern that appears in the intersection is most pronounced when both beams have the same polarization. For this figure I assumed the polarization was pointing into the screen. With an orthogonal polarization between the beams one could avoid having an interference pattern.