For general gardening op's: a Hori Hori, i.e. a Japanese digging knife. Mine was gifted and I remain ever so grateful. Great for dividing plant "root" balls (apart from the very toughest), freeing up root-bound plants in smaller pots (blade about 7" I think - mine's not to hand so can't measure) and weeding out the rooty stuff.
For tree pruning op's: a Silky brand pruning saw. (Mine's a fine tooth "Silky Gomtaro Apple" - cuts through finger-sized stems with a single backward swipe and leaves an extremely clean cut. Larger cuts no problem, but probably not with a single swipe. I mainly use mine for fruit tree pruning, but it's good for other stuff. Not sure they call the fine tooth version "Apple" any more but it is a formidable tool - mind your fingers!)
I mention these 2 tools in detail because they are, when I think about it, the 2 tools I would simply not be without. Great as gifts - gardening recipients will love you I reckon.