Well - it's some years later and.. it still seems to depend on the game the most. I play recently almost exclusively offline and connect gaming machine to Internet once every few weeks. E.g. in 'Botanicula' - with almost all achievements gathered on the way - I have only the second 1/2 of them on Steam (some of the missing ones being impossible to miss). :)
'Bejeweled 3' seems to sync all achievements perfectly (with their progress also!) on next online session. For 'Plants vs. Zombies' I have only 1 ('Home Lawn Security') on Steam while I have around 3/5 of them in game itself.
There are many threads around the web regarding those games AND achievements, but the common conclusion is: Some games just don't sync them properly and that's it. :(
I know of only one way that this can happen in windows, and has nothing to do with Steam other than their not-so-great decision to install all content into Program Files.
If you are on Windows 7 or Windows Vista, and you have UAC set to ON, then change it later to OFF, this can happen.
UAC does thing evil thing where if a program tries to write to a "protected" area like Program Files, EVEN IF YOU ARE ADMINISTRATOR, when you get a UAC prompt and give permission, it actually writes any files that would normally go into that directory into a "virtualized" directory somewhere else.
If you turn off UAC, that will no longer happen, and as an awesome bonus, it will no longer know about the files that it virtualized.
So in your case, if you had UAC on, installed a ton of games, then later got sick of UAC and turned it off, this would happen as you described.
See the second paragraph in "Features" in the article on User Account Control.
If you have done this and turn on UAC again, your content will come back, but be a TOTAL mess because if you've downloaded more stuff with UAC off, then that will be invisible when you turn UAC on, and vice versa.
this drove me a little crazy once before I realized what was happening.
i'm curious to know if this is your issue.
Best Answer
You can indeed make use of SAM to delete the achievements, the reason why playing on different pcs pushes you back to the previous state of achievements would be because you have data saved there that is different from the data you have currently.
This behavior can be also seen with games that have savefiles backed up on the cloud: In that case you will be asked if you want to keep the local or cloud save.
Assuming you can indeed succeessfully modify your achievments trough SAM you will be able to play on other pcs assuming those do not contain data that would instantly unlock said achievements.
EDIT: As long as you play on a computer that has data with achievement unlocked it will re-unlock these. this is also valid for savefiles! therefore, delete these or back them up elsewhere. in case your cloud data stored stats that the game checks to unlock these achievements, you can decide to go offline make this change and when prompted upload local files to cloud and overwrite old files. last option is if these checks are doing serverside (which i have yet to encounter but i've heard people mention this possibility before) in which case you might be out of luck, altho you could at least try using the stat tab in SAM and for example for an achievment stating
if that stat is currecntly 2k, you can lock the cahivment but since the playtime will be over 1k as soon as you open it it will re-unlock.
if you follow all of these steps correctly you should be able to relock all your achievements without issues unless they are stored server side and updated in a sensible manner for example not allowing lower values than previously recorded (which i doubt)
fun-fact: This is how, for example, from-soft checks your inventory in DS3, in this case for added stuff you are not supposed to have access to yet, not for stuff being taken away.
NOTE: not all games support steam family share, ARMA3 is one of such games, therefore the family share answer above is, in my opinion, incorrect or at the very least situational.