What do you consider to be the most important best practices for successful application consolidation?

Maybe some practical advice, within the consolidation platform you will need to consolidate not just applications but other maintenance, operational, DR schedules etc.  If you consolidate applications which have completely different operating remits then it makes standard, emergency maintenance, patching much more difficult to co-ordinate, while you gain from a reduce footprint, you lose from operational productivity.  

Many have touched on the key aspects, but let me add one more—and it's crucial. If you don't have genuine, unwavering support from all levels of the business, stop now. This means not just a Business VP giving their blessing, but also the directors, managers, and most importantly, the end users. If you can't find a single user who says, "This Application Consolidation is making my workday easier," then it's time to pause and reassess. I've witnessed many top-down consolidations that were labeled as successful, but in reality, they made things worse on the ground. Make sure your strategy is supported across the board, or you'll face an uphill battle with every application you try to streamline, with every application to try to retire.