Are most/all flights affected by a noticeable amount of turbulence?
It's very difficult to answer this question as it depends upon so many different things:
 - Location
 - Time of day
 - Season
 - Flight level
 - Terrain below
 - Current weather (of course)
 - Type of aircraft
 - The crew and their knowledge / weather radar use.

What also makes it hard is that what 'feels uncomfortable' for one person might not for another.

In the tropics it's quite common for flights to be affected by turbulence. Most will see at least some light chop. In my experience of a few hundred long-haul flights through the tropics I've only had a couple with no moderate turbulence (what you might call uncomfortable). In a similar number of short-haul flights in Europe I'd say that around 50% had no significant turbulence at all and only around 5% had moderate turbulence.

You're more likely to experience turbulence in the tropics as there's a lot more convective activity there (air rising and falling). Away from the tropics the USA tends to generate turbulence whilst Europe does not (relatively speaking). SE Asia is particularly well known for turbulence encounters.