Safari and Chrome support the basic features in recent version.
Firefox as well and any OT features called with a -moz syntax: http://opentype.info/blog/2010/08/14/better-web-typography-with-opentype...
Depending on the browser and the font-size one might need to set:
text-rendering: optimizeLegibility;

It sounds like Firefox's liga (standard ligatures) feature is on by default?

It depends on the type size.

Do Safari & Chrome have liga turned on by default?

AFAIK not. But there are extensions for Safari and Chrome to set "rendering:optimizeLegibility" for every page automatically.

Can anyone confirm the class based kerning works in either Chrome, Firefox or Safari?

It is triggered the same way as the ligature support.

HI, I'm looking for a list of features supported in web browsers, similar to the link below.
http://www.typotheque.com/fonts/opentype_feature_support

At least I'd like to know if the following features are supported in major browsers or not.
calt rlig isol init medi fina
(Sounds like Arabic, but it's Mongolian)

Here's a link to a discussion about calt in Firefox:
https://bugzilla.mozilla.org/show_bug.cgi?id=463940

As explained there, implementation has been uneven (see also http://typophile.com/node/38209).

calt should be on by default, if your font is using it for a non-default substitution, then you are using the wrong feature tag (note, the substitution can still be contextual but under a different tag, e.g. dlig, this is very legitimate).

By the way:
You can use this: http://www.impallari.com/testing/ to test open type features in web browser, and since the source code is available (here http://www.impallari.com/projects/overview/drag-and-drop-font-testing-page ) you can easily modify it to add more features for more complex testing