Aside from Skizmo's point who is right about you having posted that in the wrong forum section, actually your problem here happens to be common to both managed and unmanaged C++.

Of course a string literal that starts with a double quote (") ends for the compiler as soon as it sees the next double quote. If you want double quotes as part of a string literal (and you have lots of them here) you need to escape them by preceding them with a backslash (\).

Also, but that's not part of the reason for the errors you get, I'd recommend to remove the + sign at the end of each line of your HTML code literal. With that sign, the compiler stores each line of the HTML snippet as a single string literal and your program will later need to add them together to a single string by making callls to methods of the String class. And it would need to do that each time that piece of code is executed which is inefficient. Without the + sign, the compiler would store the entire HTML code as a single string literal that then would simply get assigned in a single step.

Last but not least, I'd recommend to add the sequence /r/n to the end of each literal line of HTML code. This would add a standard Windows line ending to the lines. Without it, the HTML code would end up being a single long line. It doesn't matter with regard to the validity of the HTML code, but it may be quite helpful when viewing the code later, e.g. when debugging.

After applying these three changes, your code would look like this:

Code:
this->webBrowser2->DocumentText="<!DOCTYPE html>\r\n"
"<html>\r\n"
"<head>\r\n"
"<meta name=\"viewport\" content=\"initial-scale=1.0, user-scalable=no\"/>\r\n"
"<style type=\"text/css\">\r\n"
"html { height: 100&#37; }\r\n"
"body { height: 100%; margin: 0; padding: 0 }\r\n"
"#map_canvas { height: 100% }\r\n"
"</style>\r\n"
"<script type=\"text/javascript\"\r\n"
"src=\"http://maps.googleapis.com/maps/api/js?sensor=true\">\r\n" 
"</script>\r\n"
"<script type=\"text/javascript\">\r\n"
"function initialize() {\r\n"
"var latlng = new google.maps.LatLng(-34.397, 150.644);\r\n"
"var myOptions = {\r\n"
"zoom: 8,\r\n"
"center: latlng,\r\n"
"mapTypeId: google.maps.MapTypeId.ROADMAP\r\n"
"};\r\n"
"var map = new google.maps.Map(document.getElementById(\"map_canvas\"),myOptions);\r\n"
"}\r\n"
"</script>\r\n"
"</head>\r\n"
"<body onload=\"initialize()\">\r\n"
"<div id=\"map_canvas\" style=\"width:100%; height:100%\"></div>\r\n"
"</body>\r\n"
"</html>";
Give it a try and let's see whether it takes you further.

Please use code tags when posting code.

Ah, and... Welcome to CodeGuru!