I do most of my day-to-day general use maps in ArcMap like I always have, but starting a few years back, the more complicated maps that needed extra graphics, tables, text, etc would be imported into Adobe InDesign (as a pdf), where I'd add the extras. You still can't do tables in a layout very well in ArcMap, and ArcMap gets flaky as you bring in more elements.
In the last year, for the fancier maps, I've begun to just use ArcMap to get my layers together (clipped or queried or whatever other GIS operations I need to do), and then use MAPublisher + Illustrator to actually make the map. And I still sometimes do the final layout in InDesign.
For the web, although we have the option to use ArcGIS Online as part of a statewide organization, I still lean towards Mango Maps. It's easy to use, quick, and I've had good support from the creator of the site. Right now its free. I like that you can password-protect your maps there.
Only other software I typically touch is Visual Nature Studio 2 for hillshading. The program won't even run on Windows 7 64bit. I have to run it on XP in a Virtualbox virtual machine software. They have a VNS3 out now, but you are talking about a lot of money for that.