Some of these may be more than you can handle, due to their aggressive/invasive/persistent tendencies. If you'd like to know how the various species will behave and play with others, we can probably give you some idea. For now, some others I'm intimately familiar with include:

-Viola canadensis
-Viola variegata (aka Viola koreana)
-Viola blanda (if you can find it commercially; more of a delicate spreader)
-Viola 'Sulphurea' (a less fragrant odorata type that seems tougher and even more willing to spread)
-Viola tricolor (common Johnny-jump-up)
-Viola striata
-Viola mandshurica

I would offer that sororia, tricolor, striata, labradorica, canadensis, variegata, mandshurica, and odorata (including 'Sulphurea') are the most aggressive of the lot so far.

Thanks for the suggestions stefanb8. My yard has zero grass, and large parts of it are landscaped in a naturalized way. The shortest plants I own are Alchemilla mollis, everything else would stand itself well above any plant in the genus Viola. Generally, the only reason for me to pull out a very short plant would be if it was growing in my walking paths, and since I mulch heavily in those areas, I'm really not even terribly concerned about that.

I would, of course, be concerned about spreaders whose roots get so dense as to make life difficult for other plants. Are any of the ones we listed between us known for being that aggressive? Thanks again!

I would be concerned about planting V. sororia and V. canadensis with anything that can't survive nuclear annihilation - but those are about the only two ;) Of course, if your soil is exceptionally poor and dry as a general rule they'll be slightly more tame, but even on moist, poor soils or dry, rich ones they could be hard on their neighbors once they formed a choking mat of growth (and canadensis is quite tall, too). It does depend upon an interaction of many complex factors, such that I've seen plants become pests in my home yard that no one else has seemingly ever had trouble with, and vice versa. Plant carefully and be prepared to intervene if necessary, but otherwise follow what your heart desires.

Thanks for all the advice stefanb8. You've been a great help!