Having been using SharePoint designer to utilize some of the more advanced features (filter parameters, conditional formatting) I can say there are definitely situations where Designer can break your pages. I've never seen it break entire sites, or external SharePoint sites, but it has, from time to time, done some damage I consider to be unacceptable. I've not really been able to pin down 100% when/why these situations occur so there's always the risk it may alter your content in a way you don't desire.
From time to time I have used the Designer Advanced Editing mode to change the contents of aspx files. Usually I modify properties of web parts using the GUI. I've found this to be a little less clunky than the Browser interface (but much different) and there are also many features of SharePoint ONLY accessible this way. There are many inconsistencies between Designer and the Browswer interface. If you feel that some of these advanced configuration options that Designer allows are something you'd like to use, or need to use, than buckle down and enable versioning on all libraries containing pages you edit. That way, when something goes wrong you can roll back to the previous working version. You may find that trying to add a certain feature is akin to "banging one's head on the wall" but atleast you have that previous version to resort to when you just can't seem to make things work and Designer decides to eat your code.
I've been using customized List Workflows created in SP Designer no problem. I've also successfully modified the new/view/edit forms using InfoPath and found this to be helpful as well. If you know InfoPath well enough you can create some forms that are actually user friendly (proper validation, conditionally filling form fields, etc) that the standard forms really don't offer.
One thing to note is that upon Publishing your latest workflow edit to the server in order to test functionality SharePoint creates a new version of the workflow. With List workflows the only way to delete previous versions is to go through the Browser interface. The ability to do seems to be absent from SP Designer. I found this out only after I got a somewhat disgruntled email from a sys. admin who asked me "Why do you have so many workflows?" I had no idea what he meant at first, and then he showed me.
Anyways. I could ramble more but I think I've illustrated my most critical experience with SharePoint designer.