How to subscribe to any or all taxonomy terms on one page?
Subscriptions
The Subscriptions module (with over 5K reported installs) is a typical solution used to setup such Subscriptions. Some details about it (from its project page):

This module enables users to subscribe to be notified of changes to nodes or taxonomies, such as new comments in specific forums, or additions to some category of blog. Once enabled, all nodes will have an additional link that allows the user to change their subscriptions. Users have tab on their user screen to manage their own subscriptions. Users can also set an auto-subscribe function which notifies the user if anyone comments on posts they have made. Admins can turn this on by default.

Total Subscription
The Total Subscription module (only a bit over 100 reported installs)  seems like a possible alternative for such subscriptions. Some details about it (from its project page):

Total Subscription provides functionality which would allow the user to subscribe to node pages, taxonomy terms, etc. The main feature which distinguishes it from other subscription modules is that it allows subscription for Anonymous along with Authenticated users.
... provides users the ability to:

Subscribe to a specific content type through the node page.
Subscribe to the related taxonomy terms associated with the node on the node page.
Subscribe to a specific taxonomy term from the term page.
Unsubscribe from any previous subscription.
Add a separate ctools content type - &quot;subscription&quot;, which could be integrated with any panel page.
Add a &quot;subscription&quot; block to the any region.


Refer to its Community documentation for more details about it, or this video tutorial (without sound ...) that takes you through various admin screens.
Apart from that, to understand what this module is about, the readme.txt might be helpful also.
Module comparison
Some more details about how both modules compare (from the Total Subscription project page):

Subscriptions provides the following features which are not there in Total Subscription, namely it allows subscription to new comments in specific forums, or additions to some category of blog. More control on subscription management for user. Users can also set an auto-subscribe function which notifies the user if anyone comments on posts they have made which can be turned off by admin. But the biggest disadvantage of Subscriptions is it does not allow anonymous users to subscribe, which Total Subscription provide. Total Subscription also has Views and Token integration.