In the late 19th Century it was very common for important games to be commemorated with a trophy ball. Basically, you would take a game ball, coat it with thick layers of paint and write on it the importance of the ball. I imagine the recipient would display the keepsake in a clubroom or other establishment so that players and fans can see it.
Below is a very early and important trophy ball commemorating the first National League Championship game in 1876. The game was between the Chicago White Stockings (who eventually became the Cubs) and the Hartford Dark Blues (they disbanded a year later). The writing says: "BALL Winning the Championship FOR 1876 - Chicago vs. Hartford - 7-6 - Sept. 26th." On top of being an important relic of the National League it happens to be the final out game ball from the event.
Who says Babe Ruth was a large oaf who couldn't use a typewriter. Apparently, Ruth's buddy, Jimmy Donahue, did. Below is a letter from the Babe to his good friend.
"Dear Jimmie, A few lines to let [you] know that Claire and I are fine and hoping you and your family are the same. It is raining like hell out and the game is called off It looks like no game today and lots of doubles headers [sic] the next trip when it will be hot as hell. I am writing this myself and it looks veryn [sic] good to me. How is every thi[n]g in Garfield. Beer is very hard to get out here and so is every thing else. will be over to see you when we get home and have some good old beer and cold cuts on those hot nights. Am writing this letter to show you that Ican use a typewriter and am very good at it. This is all for now so will see you real soon so. Sincerely [signed] Babe and Claire.
Christy Mathewson was considered one of the good guys in professional Baseball. After all, you don't get called "The Christian Gentleman" for nothing. He was an All-America Golden Boy who was both respected and loved. Christy was well-educated, having been class president at Bucknell University, and was a phenomenal pitcher. He had a career win/loss record of 373-188 and recorded 2502 strike outs.
Below is a presentation trophy given to him by the Giants for his exploits during the 1908 season.
The 1908 New York Giants were almost able to capitalize on their ace hurler's banner year—easily one of the finest pitching performances in baseball's annals, and one that would have helped the Giants win the pennant were it not for "Merkle's Boner." Amazingly, Christy Mathewson compiled a 37-11 record with 259 strikeouts, 11 shutouts, and a 1.43 ERA! The effort brought Mathewson's New York Giants within one game of the N.L. pennant, but it was the Cubs who reigned supreme that year. Nevertheless, Mathewson's monumental performance proved worthy of league-wide recognition, no organization more appreciative than his own New York Giants.
The below game used bat is something, I'm sure, most of you all remember. This is the actual bat used by Derek Jeter during Game 1 of the 1996 ALCS game versus the Baltimore Orioles when he hit that deep fly to right field that was caught by Yankee fan Jeffrey Maier. As you recall, Jeffrey deflected the ball for a home run, but it was clear from replays that the ball would have landed into the glove of Orioles outfielder Tony Tarasco. The Yankees eventually won the game, the ALCS and the World Series.