Some are achievable, even fun to get, others take an absurd amount of, for lack of a better term, "grinding", and are just a waste of time.It depends on what the developers do.
I'm a trophy whore, or I used to be; I always want to get the Platinum, but for what reason? To show off? To start a collection? What did I want trophies for? I started to have this mindset when I had bought Red Dead Redemption on Xbox 360, as opposed to my usual PS3. I had bought it because it's the better version (a lot more grass), but started to regret it simply because I would be getting achievements. not trophies. I was all torn up inside knowing that I had all my other Rockstar Games on my PS3, getting trophies for them; and this one on Xbox, achievements. I was starting to ponder taking it back, when suddenly I started to realize, trophies don't matter. I was actually take back the superior version of a game, just to get a different version to get trophies for. Why did it matter as long as I enjoyed the game? Why do cheevos matter? They're obviously there to give replay value, and challenge players, that's fine; but what about certain achievements, such as Liberty City Minute in GTA IV, where the game is trying to rush you, to beat the entire game in 30 hours or less, that makes it hard to enjoy the game to it's fullest. Or trophies that are based on complete luck; I cite Portal 2 for a lot of the following bs trophies: trophies such as Schrodinger's Catch, which requires you to catch a blue painted box before it hits the ground, but it is competely random whether or not it heads in your direction; a couple of other pet peeve trophies of mine would be: Friends List With Benefits, where you have to hug at least three people on your friends list, but what if you don't have three friends with Portal 2, then it sucks; or Professor Portal, where you have to find someone who hasn't played Portal 2 co-op, and help them through the tutorial.... fair enough, but what if you can't find someone. Speaking of which, Online trophies are the absolute worst, for people who don't have internet, who desperately want the Platinum, but can't get it, because they can't get the Thrillseeker or Buddy System trophies. Online trophies should not be required to get a Platinum. What about achievements that are to damn easy to get, such as trophies you get just from playing through each chapter of a Call of Duty game? I don't buy games for trophies, I buy them for a gripping, wonderful narrative and amzing, fun polished gameplay; and then I hear people buying an Avatar: The Last Airbender game, or a CSI game, just to get the easy Platinum, or to get their gamerscore up another 1000 points; It's dumb, to say the least. Speakng of Platinums and gamerscore, what's the point? Their essentially the same thing except that Platinums are kinda of "right now" victory, while gamerscore is a long-term victory; but your basically just trying to either get lots of Platinums or boost your gamerscore, which brings me to my next point: why are there inconsistently titled bronze, silver, and gold type trophies or randomly numbered achievement points? Your basically just trying to get either a Platinum or 1000 gamerscore, so what's the point of showing people how many bronze, silver, gold achevements you have, or why an achievement for saving the world from Satan/ Santa Claus hybrid with a mini-gun that shoots nukes, nets you 20 gamerscore; but driving your grandma to a game of senior bingo gets you 400 gamerscore. It's conflicting because nobody cares about anything you have under Platinum, which brings me to my final point: Platinum trophies and gamerscore, whether intentional or not, are just there to show how much better, or worse, you are than other people. Like somebody who has 100 billion gamerscore is a much better gamer, and person than the guy who has 1000; it (usually) doesn't mean that, usually it means that the person with 1000 spends more time playing through games, and not focusing on achievements; while the 100 billion guy focused on those achievements, spent days trying to get them, probably played through hundreds of games (most likely rich), including total garbage, just because it had easy 100%'s. I say: buy a game for whatever system you want for whatever reasons, be it control or graphics, resolution or framerate; just be sure to buy it to enjoy it, not just to get cheevos. Now, if you'll excuse me, it's time for me to go tie nuns to train tracks. See ya.
Trophies and achievements are a pointless addition to me. Why? Because like you said, some have online requirements which to people like me plagued with poor net connections, lack of friends/acquaintances/family that own the system and/or game and powercuts.
Most trophies/achievements require people to grind x amounts of kills with particular weapons; the worst offender being achievements like the Seriously 2.0 in Gears of War 2.