Full screen or more visible Skype, Pidgin, Empathy notifications?

This will implement your second suggestion. An obnoxious message right in the middle of the screen.

Go to Skype -> Options -> Notifications.

Click the Advanced View

Click for example the Chat Message Received event.

Now enter the following at the Execute the following script:

zenity --info --text "Text message from %sname."

Click Apply and Test Event to test whether an info box appears in the middle of the screen.

You can repeat this option for other events.

For Pidgin the same can be achieved using any of the execute plugin command plugins.

Recent Notifications is a GNOME applet that collects recent messages sent with libnotify to a notification daemon, such as notify-osd.

It logs all notifications that show up on your screen – whether you act on them or not.

sudo add-apt-repository ppa:jconti/recent-notifications
sudo apt-get update && sudo apt-get install indicator-notifications

At OMG!Ubuntu you can read a blog post about it: [How to] Never Miss an Ubuntu Notification