It's an interesting question, but also very hard to answer, among other things since "trouble free" is a quite subjective metric.
But we can try to triangulate some numbers:
The likelihood of having an upgrade (any upgrade) work perfectly for everyone is zero.
This is independent of which operating system we are talking about, it is merely a function of the enormous number of combinations of people, skills, use cases, hardware and software that exists in the world.
See for example
Microsoft employs 9,000 testers who test daily builds across thousands of hardware and software combinations for years before a major relase; probably noone else in the industry puts as much resources into testing as Microsoft does.
That doesn't stop problem upgrade "Windows 7" from returning 300 million Google hits (the numbers vary, that's what I'm getting at my location at the moment).
Apple presumably has a simpler job because they tightly control the very small number of hardware combinations their OS is intended to run on. Still, problem upgrade "OS X" is worth 8 million Google hits.
Ubuntu (and Linux in general) faces the same problems as Microsoft by targeting close to every hardware combination under the Sun; but unlike Microsoft they are doing so with a fraction of the resources of the major players. problem upgrade Ubuntu gives 21 million hits, while problem upgrade Ubuntu 10.10 is ~3 million.
These are obviously highly unscientific, rough and ready numbers (your Google numbers will probably be different - it varies with location, the exact phrasing of the search, and quite possibly the phase of the moon...), but I think the relative frequency of complaints can still be a better indicator than random guessing.
We need to weigh complaint frequencies against usage frequencies, hard numbers are again hard to come by.
But a random source close at hand says that Win 7 is used by 24%, OS X by 8% and Linux by 1.5% of some unspecified population. (I have no idea what Ubuntu's market share is of the Linux total, but it's almost certainly less than 100% :)
Combining these numbers with my own subjective experience and a vast quantity of anecdotes, hearsay and urban legends, I'm comfortable in believing that
- No existing software can guarantee a trouble-free upgrade for everyone.
- Upgrade troubles are more frequent among Ubuntu users than among the users of the major commercial alternatives.
- But not massively so.
Personally I always wait a few months after a release before I do an upgrade (whether it's Windows, Mac or Ubuntu) so the worst bugs can be ironed out, and I mostly have a reasonable trouble-free upgrade. And it seems to be getting better at every release, at least on the kind of hardware I am using.
To future users I would suggest that unlike romantic partners, nobody will really mind if you flirt with several operating systems at the same time.
So as long as you can spare some room on your primary drive, you can install Ubuntu as dual boot and try out an extramarital OS affair at very little risk.