Cyg OB2 is one of the most massive associations of O-type stars in our Galaxy. Despite the large interstellar reddening towards Cyg OB2, many studies, spanning a wide range of wavelengths, have been conducted to more clearly understand this association. X-ray observations provide a powerful tool to overcome the effect of interstellar absorption and study the most energetic processes associated with the stars in Cyg OB2. We analyse XMM-Newton data to investigate the X-ray and UV properties of massive O-type stars as well as low-mass pre-main sequence stars in Cyg OB2. We obtained six XMM-Newton observations of the core of Cyg OB2. In our analysis, we pay particular attention to the variability of the X-ray bright OB stars, especially the luminous blue variable candidate Cyg OB2 #12. We find that X-ray variability is quite common among the stars in Cyg OB2. Whilst short-term variations are restricted mostly to low-mass pre-main sequence stars, one third of the OB stars display long-term variations. The X-ray flux of Cyg OB2 #12 varies by 37%, over timescales from days to years, whilst its mean log(LX/Lbol) amounts to -6.10. These properties suggest that Cyg OB2 #12 is either an interacting-wind system or displays a magnetically confined wind. Two other X-ray bright O-type stars (MT91 516 and CPR2002 A11) display variations that suggest they are interacting wind binary systems.