Why does this happen?
Eclipse is an extensible software platform comprised of plugins and each plugin depends on other plugins. The successful installation of a new plugin requires its dependencies to be successfully resolved. The ideal situation is when all required plugins are already installed in your Eclipse, but this is often not the case. Therefore, the dependencies must be fetched from an update site and installed together with the plugin you actually want to install.
In order to resolve the above complex task, the Eclipse install manager (the one you invoke using the Install New Software wizard from the Help main menu) scans all update sites registered in the Eclipse workspace. The scanning process involves reading the update site's metadata and then trying to calculate the best match for the required dependencies.
The problem with getting stuck may happen for a number of reasons: the number of update sites registered in the workspace has grown significantly or there is a networking problem with the user connection, one of the update site's server, a proxy or a VPN connection.
What is the relief?
Scanning all update sites is the default behavior of the Eclipse install manager. Fortunately, it can be changed.
First, if you are still waiting on "Calculating requirements and dependencies" then hit the Stop button on the right side of the progress bar. This will immediately stop the installation process (yes - this is one of the rare cases where this button is implemented properly in Eclipse) and it will make the wizard's user interface responsive again.
Now, simply deselect the "Contact all update sites during install to find required software" checkbox. This way the install manager will look for dependencies only on the update site providing the plugin being installed. None of the other update sites, registered in the workspace, will be contacted. This will significantly improve the time spent on the "Calculating requirements and dependencies" phase and it will reduce the size of the metadata that needs to be downloaded.
There is one drawback of deselecting the checkbox. If the update site providing the plugin being installed is not self-contained, i.e. does not provide all the required dependencies, then the installation will fail with an error message for unresolved dependencies. However, this will be a fast failure and you can go back and select the "Contact all update sites..." checkbox again. In such case, I also recommend to go and review all registered updates sites in the Install/Update > Available Software Sites preference page and disable those that do not seem to be related to the plugin being installed.
My personal experience is that the majority of Eclipse plugins install without any need for scanning additional update sites for the required dependencies. My recommendation is to deselect the "Contact all update sites..." checkbox and select it only if the installation process fails without it.
Is there such an option in the Eclipse Marketplace Client?
It's nice that the Install New Software wizard provides a checkbox that can be deselected, but why can't you find a similar checkbox in the Eclipse Marketplace Client?
Well... because you don't need one. The Eclipse Marketplace Client is a smarter and user-friendlier version of the Install New Software wizard. It implements a fallback strategy - first, it tries to resolve the dependencies by only looking at the update site providing the plugin, and only if that fails it will automatically try contacting all update sites.
Effectively, this is an automated implementation of the recommended manual workflow given above for the Install New Software wizard. In case you are curious about the details regarding the implementation of the fallback strategy, you may have a look at the discussion in bug 316362.