Rule to send out content of newly created forum-topic or comment
Using rules, you can send the URL of the updated content as per the solution provided by @mohit_rocks, but I was not able to find a solution to send the content / body (full / teaser) in the mail, using rules.  

If you wish to send the content of the body too, you'll need to take help of the Notify module.

Steps to enable the send mails with the content of forum/topic in mail with the help of notify module:


Download and install notify module.
Under admin > people > permissions, set give the permission of access notify to the user role you wish the mails to go to. Note: The users of these roles need to enable the notification to enable receiving of the mails. You can keep this role limited to admin and let admins decide who receives the mail by following next step.
Go to admin > config > people >notify and enable notification for forum content type:  If you set time less than the time of your cron run, still the mail will be sent on cron run.
Go to user > uid > notify (replace uid with the the user id of the user). Admins can go to admin > people select edit against any user, and go to Notification settings tab and check the following options:   You can check the Title + Body + Fields under Detailed settings section to send the values in fields as well.
To check the list of users who will receive the mails, go to admin > config > people > notify > users:
That's it! Now the selected users should start receiving the notifications mails with content!


Note: If you have revisions enabled for the content type, and want to be notified when the content is edited, then check this feature request I've made at the module's issue queue. I've also created a patch for the same. If you have such requirement, then you can test the patch. If you post your findings on the issue, it'll be appreciated!