As you may know, Richard F. Outcault created the Yellow Kid in 1894. The following year, the character got his own comic and quickly became successful. Outcault took the character over to another paper in 1896, but his original publisher hired another cartoonist to continue the strip. Both strips continued until 1898 when the character's popularity faded.
Outcault did a variety of cartoons for the next few years, and then debuted Buster Brown in 1902. That also became popular. In 1906, Outcault again took the character to another paper, but his original publisher again hired a new artist to continue the strip. This time, the original strip (under a variety of artists) fell by the wayside in 1911, while Outcault's version continued on through 1921.
Now, here's the interesting bit. Twice in 1907 and two more times in 1910, Outcault's Buster Brown strip featured the Yellow Kid as another character. Not just in a small cameo either, but in a significant co-star role. In fact, in these appearances, the Yellow Kid speaks in 'standard' word balloons -- something he never did in his own strip! (Frankly, seeing him speak seems a little strange to me.) It's by far the earliest comic character crossover I've ever heard of.
Here are the first and (I think) last of these appearances...
I'm not totally shocked as Outcault was the creator of both characters, and I can see why he might think it'd be fun to throw these two characters together. But here's (for me) the kicker: the original art for Outcault's second crossover strip still exists! It was sold at a Heritage Auction in 2005 for $25,000. It's given continuity by referencing the two characters' first meeting, and the dream state is again emphasized with the maid reciting "Now I Lay Me Down to Sleep." And will you just look at the gorgeousness of that bottom tier of panels?