When using a $n$-bit hash, the probability that an accidental change goes undetected is about $2^{-n}$ (for hashes that even mildly meet their design goals).
If one is using this technique once per second for 100 years, with a 128-bit hash like MD5, that probability is $36524\times86400\times2^{-128}\approx2^{31.6-128}=2^{-96.4}$.
We know of 44 craters on earth caused by collision with a celestial body large enough to be a major blow to our current civilization, that occurred within the last 2.3G years. Thus probability of a civilization-disrupting event within this 100 years time-frame is at the very least $44\times100/(2.3\times10^9)\approx2^{-19}$ (and I'm optimistic here: man-made nuclear obliteration is arguably more probable). Thus there's no point in bothering about a probability of only $2^{-96.4}$.
But in cryptography, we consider adversaries that actively try to defeat us. If we use a 128-bit hash (such as MD5), and make many files (say $2^{31.6}$ as above, which hashes fit a 64GB USB stick), and have powerful adversaries with the kind of resources wasted in bitcoin mining¹, then the possibility that they find a file with the same hash as one of ours becomes sizable (though not the the point I would be bothered).
The real and immediate danger comes if we assume the adversaries manage to penetrate the software we use to save our (say PDF) files, and we are silly enough to use MD5 or SHA-1, which chosen-prefix collision-resistance is broken. Now adversaries can effortlessly produce files with the same MD5 or SHA-1 as any of ours, that look exactly how adversaries see fit when viewed.
For my purpose (just data validity check), what would you recommend?
Ignoring the possibility of adversarial modifications is off-topic in a crypto group. If we do this, a CRC is enough. 64-bit is fine. About the only thing to fear is that the media could internally use a CRC, and they interfere. For lack of information, choosing a random 64-bit primitive CRC makes sense.
Back to cryptography and it's adversarial model: it should be used unbroken hashes like those of the SHA-2 or SHA-3 familly. Short of a breakthrough that few expect, SHA-256 is adequately secure for likely at least a decade, SHA-512 forever (at a human scale) even if we assume we ever get Cryptographically Relevant Quantum Computers.
¹ I'm talking about the overall electrical power and integrated circuits wasted. The bulk of it would however not be for massively parallel hashing with ASICs as in bitcoin mining. It would be for fast memory organized for search, since computing MD5 hashes has low cost compared to matching them with the $2^{\approx31.6}$ target hashes.
