Having trouble escaping quotes and braces

Do not use single quotes. Escape any double quotes within the string with a \.

curl -X POST -d "{ \"method\" : \"account_info\", \"params\" : [ { \"account\" : \"rHb9CJAWyB4rj91VRWn96DkukG4bwdtyTh\"} ] }" http://s1.ripple.com:51234

Window's command.exe doesn't seem to support single quotes. PowerShell does, but there are still some problems when using them, so the best solution is to not use them at all.

You can use curl -g to turn off globbing:

curl -g -X POST -d '{ "method" : "account_info", "params" : [ { "account" : "rHb9CJAWyB4rj91VRWn96DkukG4bwdtyTh"} ] }' http://s1.ripple.com:51234

Easier than escaping all those brackets.