Can crossing over between X and Y chromosome of sex chromosomes take place?
Yes, it can, but it is rare, and typically only in the pseudoautosomal region, meaning those sections on the X and Y chromosome that have homologous genes.
The reason it's rare and more difficult is that the DNA does not match as well, so the chromosomes have trouble interacting along the length of the chromosome.  Furthermore, there are less recombinant zones available.

Sources:

Kauppi, Liisa, Marco Barchi, Frédéric Baudat, Peter J. Romanienko, Scott Keeney, and Maria Jasin. 2011. Distinct properties of the XY pseudoautosomal region crucial for male meiosis. Science 331 (6019): 916-20.
Hinch, AG, N. Altemose, N. Noor, P. Donnelly, and SR Myers. 2014. Recombination in the human pseudoautosomal region PAR1. Plos Genetics 10 (7): e1004503.