I feel like I always see 「しまう」 at the end of sentences (not the verb "to put away"). I saw some examples here on Weblio.
どうしても写真は実物より劣ってしまう。 Pictures really don't do it justice.
私はどうしても彼を目で追ってしまう。 No matter what happens I keep following him with my eyes.
「私の場合、どうしても溝口健二と比べてしまう。」 I can't help but compare him to Kenji MIZOGUCHI.'
I thought it's basically like 'can't help but', but then the first example seems different.
Anyone have more examples of this? What exactly does it mean?
I think the most basic meaning in English is "wind up" or "end up".
That seems to work for all of your sentences:
どうしても写真は実物より劣ってしまう。
Somehow the photo always winds up being inferior to the real thing.
私はどうしても彼を目で追ってしまう。
I always somehow wind up following him with my eyes.
「私の場合、どうしても溝口健二と比べてしまう。」
In my case, I always somehow end up comparing him with Kenji MIZOGUCHI.
I think there's sometimes a sense of disappointment as suggested in the other answer, but I don't think that's ubiquitous (If I'm wrong, I look forward to learning).
This use of しまう is like adding "regrettably", or "unfortunately". It means that the action given in the て form is not a good thing.
The fact that pictures don't do somebody justice is not a good thing. So they end the sentence with しまう.
ああいう話{はな}し方{かた}は、人の年齢{ねんれい}をさらけだしてしまう。
"That style of speaking reveals a person's true age, unfortunately".
This means that there are bad overtones to the person's age becoming known. For example, the style of speaking reveals that he/she is too old or too young in the speaker's opinion.
