To get the manufacturer ratings - click on the "View Product Specifications" for some of the contact's details pages (you can also get to the details page by clicking on the "details" button... but for some reason, that always gets overlooked).
Note that the 0.062" and 0.093" connectors are tougher to get a current rating. The number of contacts within the plug footprint and the arrangement affects the current rating. For example -- a 3x3, 9 pin plug -- if the center conductor is surrounded by high current contacts (potential heat sources) then his current rating is reduced.

The 0.156" Molex 45570 series contacts are rated up to 13 amps but are somewhat tough to crimp properly.
The AMP version (forgot the part number) has similar ratings, cost more and are also somewhat difficult to use.

Jones plugs... no idea, never did find a datasheet for those.