How much data can I store in a cookie
Here are the limits according to 'browser cookie limits':
Chrome & Firefox - No limit to the number of cookies; limit of 4096 bytes per cookie.
IE8-10 - 5117 characters per cookie; limit of 10234 characters.
Safari on Mac - 4093 bytes per cookie. Limit of 4093 bytes.
Safari Mobile - 4093 bytes per cookie. Limit of 4093 bytes.
Android - 4093 bytes per cookie. No limit.
Source: http://browsercookielimits.x64.me/#limits
I'd say if you have a destkop application, to be bound by the limits of IE or even Safari if you have Mac users. If it is on the phone, than definitely just 4093 bytes. If you need more, you are going to save to the server or create two different experiences for Safari / IE and Firefox / Chrome users.
To comply with the standard, you should store no more than 4096 bytes per cookie.
Another point worth remembering is that cookies are sent on EVERY request to the matching domain, which is very significant overhead in the case of a sizable cookie (upload speeds are often 10x slower than download speeds).
As to specific limits per browser, I defer to another response.
This can be also helpful here: