I assume you mean Limit Dimensioning per section 2.2 of ASME Y14.5M.
In the UK where I worked we normally did limits, e.g. .995 to 1.005. Here in the States the place I work mostly uses +- e.g. 1.000+-.005.
I'm not sure there's any widely accepted method of determining which to use. +- Dimensioning is perhaps better for manufacturing, as it gives them a nominal/mean to aim for without calculation. Limits is perhaps better for inspection since it's obvious if a measurement is more or less than the limits without calculation.
However, the calculation is so trivial I'm not sure it's much of an argument, but I suppose for every calc there's a chance of a mistake.
Now as regards non symmetric +- dimensions, the most obvious example I can think of is typically drill tolerances. Depending on size these will be +.005 -.001 or similar, essentially the nominal size of drill tends to produce an oversize hole. This Tolerancing method is to allow easy selection of standard size tools while allowing for the fact that the hole will be oversized. The same idea may be extrapolated to other processes etc, perhaps some types of semi stock dimensions or the like.
I know some people use non symmetric to imply they'd rather be at one end of the range than the other. For instance if they'd like to have a .5 dimension but if push comes to shove they'd accept up to .51 then they'll dimension it .50 +.01 -.00 rather than .505 +-.005 with the hope that most of the parts will end up nearer .5 than .51. However, to the best of my knowledge this idea of preferring one end of the tolerance zone is not supported by the standard, if the entire tolerance range is acceptable then it's acceptable, if not then a tighter tolerance should be specified.
KENAT,
Have you reminded yourself of faq731-376 recently, or taken a look at posting policies:
What is Engineering anyway: faq1088-1484