8 Megabytes
Do note that the limit is in computer scientist slang megabytes or 8*2^20 bytes and not 8*10^6 bytes (the actual meaning of megabytes).
This difference is minor but is very confusing to some people and is why you can see maps a little over 8,000 KB online (as the limit is 8,192 KB).
The reason why Computer Scientists use 2^10 instead of 10^3 for storage related sizes is it is far easier to work with on binary systems.
It has been raised since the initial release of WC3 by a patch so older threads and sites might tell you the old map size limit which no longer applies.