Considering that there is a seemingly easy lossless transformation path from/to these full-width/half-width alternatives, it would suffice to only support the full-width form one would think (and do some transformation as necessary without the user being involved).
You'll want to use half-width for full number fields because html number input is half-width, and you'd need to move to the "full" alpha numeric keyboard to get full-width. Also if you allow full-width it opens the door to Chinese numerals, which you'd have to convert as well.
Same thing for email address fields, allowing full-width character is user-friendly but you're pretty guaranteed to have no autocompletion on the user side, you deal with weird validations errors as some users will mistakenly convert part of the address to invalid chars, when forcing half-width pretty gets rid of that class of error altogether (assuming you don't allow full-width mail addresses in the first place. If I'm not mistaken they can be valid, including with a full-width domain)
Places where there's less room for error usually allow both (like addresses for instance, where you won't run any validation on it anyway. Except on old sites and anal retentive services that will force you to go full-width sometimes)