I would never get my genes sequenced--not because I'm scared of what I might find, but because of the possibility of changing them.  I've never actually heard anybody talk about this aspect of DNA sequencing before, but it was the first thing that popped into my mind when I first heard about it.

In case you're not familiar with it, the observer effect is a completely bizarre but effect in quantum physics that says observing an outcome collapses the probability wave into a single outcome.  In other words, the simple act of observing something causes a single outcome to become reality.

For gene sequencing, this means that as long as your DNA remains unobserved it is still a cloud of potential.  As soon as you observe it, though, you're locked into a specific outcome--a specific gene sequence.  This means that sequencing your genes might actually affect them.  For example, if alzheimers in my genes is a possibility, sequencing my DNA might actually make it real.  Why would I take that risk?

For a nice easy-to-understand explanation of the quantum observer effect, check out the following video.  I highly recommend taking a look if you're not familiar with it.