Anyone want to take a stab at this?

[Proud Public Servant]

7. Can I play? I love this sort of stuff

Internationally
A loss in the Spanish-American War would have left us without possession of either Guam or the Philippines; without Guam or the Philippines, we would have had no way to project power into the Pacific. Thus, there would have been no reason for Japan to attack us at Pearl Harbor.

The consequences of this are considerable. We would have entered the war later, fighting only in the ETO. This probably would have concluded the European war more quickly (because we could throw all our resources at one theater), but would have allowed Japan to empire-build unencumbered. It also would mean that we wouldn't have dropped the atomic bombs.

What would follow would be an uneasy peace with Japan, that would thaw into an alliance of convenience once Mao came to power in China; the oppositional Asian power there to check him would suddenly be our best friend.

Bonus: no Vietnam; that would be Japan's headache.

Domestically
The loss would almost certainly turn the Republicans out of office in 1900, and with the election of Williams Jennings Bryan -- a populist anti-imperialist -- U.S. politics would have taken a decidedly different and more radical turn. Faced with Bryan, it's hard to imagine the Roosevelt-Taft progressive wing of the GOP exercising any dominance (indeed, it's entirely possible that Theodore Roosevelt might not have come to national prominence at all), and thus hard to imagine any significant influence wielded by middle-class progressives (who were by-and-large Republican). Instead, a shamelessly pro big-business GOP might well emerge 20 years ahead of schedule -- but as a minority party -- and US politics might take on a more decidedly European, class-based cast.

Most depressing possibility: without TR, no FDR.

There, that was fun.