My favorite filler foliage is bronze and/or green fennel of which I grow a number of clumps for just this purpose. Perennial, long lasting foliage in water, soft, feathery. Compliments any arrangement.

Bupleurum is an early blooming annual here, a friend gave me some seeds and I love it. Very interesting.
Other great fillers: ammi majus, nigella in flower and then it's pods: both the 'regular' types and the 'transformer', fennel I have to agree with, dill in season (short season), alliums of all kinds, erigeron: "Santa barbara daisy" is the common name, white obedient plant, white goose neck loosestrife (which I grow in tighter clay and a little dry to keep it in line), Tovara "painters pallete", talanium, batchelor buttons, basil (I get the types which have lovely flowers), rosemary, wheat celiocia, last year we successfully grew lovely stocks - AM sun, PM shade in well drained soil (the year was not overly humid)...

I have certain shrubs in the yard that are my go to plants for greenery but I usually use them most in fall and winter when flowers are sparse or I want fillers for store bought flowers.
Hinoki cypress is my favorite.
Grey Owl juniper
Chindo viburnum
Rosemary
Curly ligustrum- I love it in bud
And, yes, wild privet- I like the berries. It's in all the undeveloped places around the property but I don't plant it, of course.

Ones I have used with beautiful results are artemisia and hosta leaves