We actively ban relatively few plugins, but we continually update our banned plugin list, and reserve the right to remove troublesome plugins at any time. Whilst we're hosting your site in a very powerful system, we must make sure that your site doesn't impact others, and that other sites can't impact yours. Here's some types of plugins we'd like you not to use.
We already have a very advanced caching system in front of your site, so any caching plugins are likely to not improve your websites speed, and may actually slow it down.
Abandoned or unmaintained plugins are dangerous. If a security vulnerability is found in one, we may have to disable it across the board. If a vulnerability is found in a plugin, and patched, we may push the patch to all users of that plugin. If we can't patch it, leaving it active is a threat to your site; it's best to avoid using plugins that aren't being actively maintained.
Other hosts function
Other automated WordPress hosts, including ourselves, deploy plugins to override certain functions within WordPress, to make your site work best in our environments. You can copy these over to our services, but they might cause your site to do odd or unwanted things.
Backup plugins that store backups locally aren't really needed -- we take a backup automatically daily. They tend to use a lot of diskspace -- which we do limit you on!
If you want, however, feel free to use a plugin to backup remotely! VaultPress for example is known to be very good.
This is a bit of a grey area. Any plugin which uses a lot of system resources is bad. Related post plugins, for example, tend to use a lot of resources. However, if one of these plugins is heavily cached, or you're not receiving a lot of traffic, it may be acceptable. Generally speaking, bear in mind that you're sharing some resources with others, and them with you.