In the vast majority of cases I'll watch the cut scenes, if not it's a bad sign. I like quality games with well-written plots, I also like games which are all-game and no plot, but I don't like games with crap plots or non-games with almost no game in them. Excessive cut-scenes can and do ruin games for me and can also make a mediocre or bad game worse.
FFX is one example, I wasn't enjoying it anyway, but the cut-scenes were forcing more of the god-awful plot and characters down my neck. At the point when I hit eject I remember there being one cut scene which bored me to tears, when control of mop-head was returned to me I ran him around a corner and up a small flight of stairs, then the next cut scene started, eject eject eject. Put me off FF.
Plot being delivered by journals or 'radio' is hackneyed now, but I think BioShock 1 & 2 did brilliantly with the latter and Resident Evil with the former ("itchy.... tasty!"). Sometimes a handful of cut scenes really adds to a game, Haunting Ground's cut scenes are short and infrequent, just enough to fill you in.
I definitely do like plot, but I'm not in with the "it's all about the narrative" indie luvvie-duvvies and clueless triple-A studios, the former pumping out non-games and the latter overblowing their plot delivery well beyond the writers' ability to maintain pace. This War of Mine is another example of less is more, it's got character bios and short chats with NPCs, that just fills in the blanks and makes you care, but it doesn't try to grab you by the skull and yell "look, LOOOOOOOOOOOOOOK, we have a tale of sorrow to melt your blackened heart". Subtlety is lost on so many devs these days.