This period, from the perspective of military operations and wargaming potential, is fantastic. It is the century that sees musketry evolve from a weapon of mass application (with little precision), into the dominant force on the battlefield (as we evolve from the age of muskets, to the age of rifles). The introduction of the railroad and mass production also mean that armies and logistics are evolving, so that operational campaigns are very different. Naval capability changes from being wind and muscle driven, to being steam driven - which means that imperial and global colonialism is not only possible, but commonplace (with the colonial wars that go along with it).
I will include in this listing a few armies from the very early (pre-WW1) 20th Century.
This is a big enough collection to put on a 6-8 player game. Maybe a thousand Mexican figures, and maybe eight hundred Americans and Texans. All painted, recently rebased.
This is a larger scale (in terms of larger scale battles) and more serious study of the two parts of the River War (as Churchill called it) than my 28mm TSATF collection ( which is, appropriately, for small scale skirmish engagements). I have British (painted), Egyptians (unpainted, but also suitable for the Arabi Revolt), and Mahdists (hundreds painted, but hundreds not painted).
Probably not worth mentioning except for an impressive stash of very nice, but unpainted, Zulus. Hundreds of 'em.
American Indian Wars
This is a recent acquisition for me, a set of very nice (but individually mounted, so suitable for skirmish gaming) figures including US cavalry forces (mounted and dismounted), and a large selection of American Indian figures. There are leaders and a variety of figures for both sides. I have not gamed with these yet, but I am planning on trying The Tomahawk and the Flame, Pony Wars, and/or Hey You in the Jail (one of my favorites, now available as a PDF download).
Spanish American War
A few years back, Patrick Wilson re-released the Richard Houston Lyzard's Grin collection. I bought in. I have a few hundred figures, all painted nicely by John Callahan. Both sides, and big enough for a modest game. No Philippines or Moro figures.
Very nice Old Glory 15s, this is at heart a nice, large collection of unpainted Boxers, and some Europeans. Started this collection to take advantage of Americans (from above), and Russians and Japanese (both from below).
Another nice OG15s set, painted (by me) and large enough for a meaningful game. Maybe a dozen infantry units per side, with 2 or 3 cavalry and artillery units for each side. Many more troops for Russians. In addition, maybe another dozen units each side, of infantry.
This series includes
Part 6 - 19th Century (this article)