You don’t even need an IDE – you can use “Object.watch()”:
If you use any one debugger, I’d strongly recommend Firebug. For all your Javascript, HTML and CSS needs :-):
http://getfirebug.com/javascript
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Update for 2019:
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Object.Watch is Ancient History. Uncoincidentally, it’s unavailable in most contemporary browsers.
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My personal favorite JS debugging tool these days is Chrome Developer Tools.
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My personal favorite JS IDE (for Angular, .Net Core, etc) is Microsoft Visual Studio Code (MSVC).
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You can do just about any “expected” debugging operation – including set watches – with the Chrome debugger (just as you could with FF Firebug).
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Chrome debugger is well integrated with the MSVC IDE.
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Both are “free” (at least “free as in beer”); both run well on Windows, Mac and Linux.