It's a bit strange to talk about an history of the "trumpet", an instrument that has changed probably more than any other throughout its 4,000 year history. But here goes:
If you want to talk about earliest ancestors, you have to mention the Shofar and other vague animal bits into which people first blew, hoping to amplify their own voices. China, Tibet, Japan, Palestine, and Egypt all had their own versions, all following rather closely on the heels of the first percussion instruments. cf. these two biblical passages: Leviticus 25.8-9, referring to the Jubilee year:
Seven weeks of years shall you count-seven times seven years- so that the seven cycles amount to 49 years. Then on the tenth day of the seventh month let the trumpet resound; on this, the Day of Atonement, the trumpet blasts shall echo throughout your land
...and Numbers 10, God speaking to Moses:
Make two trumpets of beaten silver, which you shall use in assemling the community and in breaking camp....It is the sons of Aaron, the priests, who shall blow the trumpets; and the use of them is prescribed by perpetual statute for you and your descendents
Already, we know we're no longer talking about ram's horns for the shepherds. The trumpet, probably a strait metal tube, usually of silver or bronze, with a bell at the end, capable only of the natural tones. The trumpets found in Tutankhamun's tomb, probably similar to those described in the bible, are roughly 120 cm long, with a bell diametr of 26 cm. The passages both indicate use for celebration as well as communication, and indicates a quasi-religious significance. cf. the following from the much later book of Revelations, 8.1:
...and I saw seven angels who stood before the Lord, and seven trumpets (salpinges) were given to them
where each blast in turn, heralds the destruction of the earth.
Let's turn now to Greece; the same word in Revelations is used in the Iliad of Homer, book 18, line 219: ...He cried aloud...piercing as the battle-cry of the trumpet which blasts from raiding hosts besieging a city. A 5th century image of a Spartan hoplite show him blowing a trumpet, roughly a metre long and with a much smaller bell than the Egyptian.
In the ancient Olympics, beginning in the 96th games of 396 B.C., there was a trumpet competition. A known trumpeter, Herodoros of Megara's career spanned some 40 years, with 10 successive victories; he is said to have played for king Demetrios Poliorketes, encouraging his troups in battle with his playing.
The trumpets of the Romans were much more varied; the bucina was a curved instrument, the tuba the straight tube of the Greeks. Aside from their uses in war, they were often used to herald the changes of the hours. Instead of ad primam vigiliam ("at the first watch"), we often find ad primam (or whatever number) bucinam. Cicero also mentions their use in calling assemblies: bucina datur: homines ex agris concurrunt
This all changed very little in the Middle Ages; despite the fact that trumpets, which were thought to mimic/amplify the workings of the human voice, were among the few instruments that could be played during mass, and were used to announce royal arrivals, trumpeters were pretty damn low on the social scale. Finally, in the 16th century, trumpeters somehow figured out that at the higher ranges, the overtone series notes were much closer together, and something close to music, as opposed to the same bloody fanfare over and over again, could be played. This soon led to the formation of guilds and academies, something of a band geek mafia to regulate membership and keep the thing elite.
The 18th century saw further improvements; rejected from almost every string-ensemble or chamber concerto because of its tendency to drown out everybody else, the trumpet got it's first real make-over. Key-pitch was standardised, usually to D or E flat, and a shallower mouthpiece allowed for easier play in the higher ranges. Already, Leopold Mozart and Michael Haydn were producing trumpet concertos in the softer, gentler clarino style. Around this time, too, somebody first hit on the idea of curving the tube, reducing the risk of decapitating somebody with your 2-metre-long trumpet during a particularly rousing solo.
Early attempts around this time to make a "key" trumpet failed miserably. One model simply added saxophone-like keys to the tube. Another, the precursor to the trombone, added a sliding mouthpiece, rather awkward and particularly slow. Thanks to the utter decline of the old school nobility and the rise of democracy, the trumpet, ever connected with royalty and the court, suffered in popularity. It took true marketing genius in 1813 to add actual valves, though the new-found ability to play a full scale didn't do much at first.
A brief overview of the piston valve (not those funky rotary valves those French Horn players use). With none of the three valves depressed, the air through the tube travels the shortest possible distance out the bell. Any one valve reroutes the air through another side-tube, lowering the pitch. When more than one is pressed, the air flows through each one in turn. Genius, huh?
Stiff competition from the more tonal and accurate B-flat Cornet led to the development of the B-flat trumpet, the one still used today.
Around this time, in 1825 in Lyons, was born one Jean Baptiste Arban, the grand-daddy of style (or should be) to every trumpet player; he layed out a Complete Conservatory Method for Trumpet, describing the instrument and setting exercises to master the beast. If you really want to learn 18 different ways to triple tongue the Blue Bells of Scotland, he's your man (or was; he died in 1889).
The twentieth century saw a bit of a revival for the poor trumpet. A complete make-over, years of hiding in basements triple-tongueing until the tongue went numb, and the rise of swing, jazz, and ragtime brought the trumpet back to the scene. No longer was the trumpet shoved in the back of the orchestra and given all the uninteresting bits (except in Wagner); he ruled the big bands. Even better, jazz let the trumpeter improvise freely, unchained from the score and free to show a full range from the low F-sharp to the highest of double-high-C's. Louis Armstrong, Herb Alpert (with his weird brand of slightly off-pitch and off-rythmn synchronisation), and Leroy Anderson have done much for it.
Contrary, however, to Mr. Crux's statement, the trumpet is not a hallmark of ska. The first wave saw more trombones and saxophones then trumpets, with exception of only a few pieces like Don Drummond's Down Beat Alley or the Skatalite's Lucky 7. They are almost completely absent from the 2nd wave, which is ska only by virtue of some downbeat-calypso rythmn played on hammond organs.. Only in the newest re-incarnation, 3rd Wave Ska, has the loud brass and the fast lick become important.
To quote Reel Big Fish: was that too much? I never know...