Games, especially RPGs, that don't give immediate gratification (where you slowly grow into doing the cool stuff over dozens, or hundreds, of hours) are going to be popular choices for "most boring" from most gamers who frequent these forums. Casuals being casuals, even if most don't see themselves that way, and casuals all wanting immediate, constant gratification or "it's boring, and sucks".
To be entirely fair there are so many boring games out there that it's very easy to pick some and it's hard to pick "most boring" as a result. I'd pretty much have to nominate any "Arthouse" game, most of which themselves state they aren't trying to be entertaining. These games can involve things like watching some guy sit in a cemetary, following some philosopher around as he espouses his theories on life, walking down a cooridor, watching surreal images, or taking a walking tour of an island while a narrator implies mysteries and answers which really aren't there. Oftentimes leading to discussions as to whether a lot of these works are "Games" at all given the lack of interaction or attempt to entertain, but they bear the label now, so I figure they count.
I pretty much figured I'd mention them as prattling out names (Cooridor, Dear Esther, etc...) would probably become a pretty big list.
Then of course there are legions of really bad visual novels out there along with the good ones, really repetitive hentai games, and things like that. Not to mention "edutainment" games with titles like "Math Blaster" or whatever.
In general if the guys designing the game tell you it wasn't intended to be "fun" it's not. The people who rate these things highly usually admit to being bored to tears, but do so because of the innovation or eventual long-winded point. Progressing games as art being more important than whether they entertain you or not. Sort of like some butt-ugly masterpiece painting which demonstrates some kind of color contrast or stylistic visual trick more than trying to be pretty/cool/entertaining. You know like... multi colored lines on a canvas... or some dude who threw buckets of paint at a canvas while on LSD and then probably managed to sell it to someone with money who was high enough on shrooms to think it talked to them or something, and then talked it up to try and justify it being worth hundreds of thousands of dollars later (which is frankly the only explanation for some of these paintings that could possibly make sense to me).
