We have just finished a cosmic radiation survey at work.
Conclusions, at the current flying rate, no one will exceed the limits set out by the authorities. Even if we were doing 900 hours a year, no one would exceed the limits set.
There are a few limits to concern ourselves with.
At 1 mSv (Sievert) a year, aircrew must be notified of that exposure and the possible risks. (Done at Indoc).
The next limit is 6 mSv a year. If you exceed that you then must be individually monitored and rostering changes actioned to reduce your annual exposure.
Off the top of my head the overall annual limits are 20 mSv a year for every one. This takes into account the average 2 mSv a year every one is exposed to from good ol' radon. Radon is emitted from rocks. We get exposed to it by stone buildings or brick buildings. Easiest way to reduce the exposure is to get some fresh air circulating. If you live in a particularly rocky area ie, with big deposits of granite etc, you may get more of a dose.
The sievert measures "how much of an impact it has on living cells". 1 Sv is equal to 100 rem.
If we can keep the dosages low then generally, our body will repair the cellular damage. So your mother's advice about eating healthily and getting a good night's rest is still valid.
As neutrons form the greater part of the exposure at altitude and their effects not that well known versus other alpha particles, the general advice is for pregnant women not to work as aircrew.
Will cosmic aka ionising radiation acquired whilst airborne cause male sterility or genetic problems? Probably not. Men generate millions of sperm often with an average life span of 3 months. That is, if the little wrigglers aren't expelled in the mean time.
As stated by a previous poster, it's the Earth's magnetic field that does most of the shielding from cosmic radiation.
2 flights stood out as a great example of the difference that latitude plays.
Both 10 hour flights, both at around FL430/FL450.
Geneva to Capetown. 35 uSv (micro, ie 1/1000th of a milli mSv)
Stockholm to New York. 145 uSv.
If you're stooging around below FL200. You have nothing to worry about.
Between FL300 and FL400 around Europe, again, the dosage rates are very small.
Blasting for 10 hours on Polar or near Polar routes? Then you'd need to do about 60 such flights a year before you'd get close to the 6 mSv limit.
To put it into perspective, as talks about ionising radiation tend to alarm, you'd have to be exposed to 6mSv a year for 30 years to increase your cancer risk by 1.2%.
So, to answer,
No, no, no.
FAA source
Calculate your own dose
Skybrary doc