Usually a plugin developed in WordPress version will run fine on several newer versions. What you need to care about is ‘deprecated` features/apis in WordPress. Any API in WordPress is not removed overnight, rather it remains deprecated for several versions. You will get such a list here:
http://codex.wordpress.org/Category:Deprecated_Functions
When you develop a plugin, you can see what are the specific api you are using on your plugin and which WP version introduced that API. That should be the minimum WordPress version your plugin require and you should mention it clearly on the readme.txt.
After development, you can test on several backwards and available forward releases. For example, when you are developing a plugin on WP 3.1, you can also check whether it works on versions below 3.1. Again, first check which you API you are using! You don’t need to check WP in version 2.7 if a API is introduced in version 2.8 as it won’t work (unless you plan other alternative).
Then you can check any current stable releases greater than 3.1. If nothing available, you can check the alpha/beta/rc versions of the new WP. You can check their upcoming changes on roadmap.
When newer WP version is available, you should immediately check if the plugin is working as expected. If not, make a new version of your plugin and commit to repo. When people will see that your plugin is not working on new WP version, they are supposed to check if the updates are available. If you tag a new update of your plugin, it will notify users about the update on their plugins page.
I hope these info helps, at least a bit :-).