There are numerous accounts of the Crusades written by people who participated in them. In fact, they form a major source for our information on what occurred on the various Crusades (from the Western perspective, anyway). They're generally written after the fact (although in some cases they may have been begun while the Crusade was still ongoing) with the power of hindsight, so they're not exactly like a journal would be, but that doesn't make them less interesting to read.

For the First Crusade, there are three and a half major eyewitness accounts (I'll get to that half bit). They are:

There are numerous accounts of the Crusades written by people who participated in them. In fact, they form a major source for our information on what occurred on the various Crusades (from the Western perspective, anyway). They're generally written after the fact (although in some cases they may have been begun while the Crusade was still ongoing) with the power of hindsight, so they're not exactly like a journal would be, but that doesn't make them less interesting to read.

For the First Crusade, there are three and a half major eyewitness accounts (I'll get to that half bit). They are:

Fulcher of Chartres: Possibly the most readable account of the First Crusade, and probably the most comprehensive single eyewitness account. Fulcher was a French priest in the service of Baldwin of Boulogne (the future Count of Edessa and later the King of Jerusalem), and his account primarily follows Baldwin’s adventures. This is important because at one stage Baldwin separated from the main Crusader army, and Fulcher followed him, giving the only eyewitness account of these events, but also missing several important moments in the main campaign due to his absence. He includes accounts of these events in his chronicle, but we know he did not see them himself. Fulcher’s account extends beyond the end of the First Crusade, and into the reign of Baldwin II, making this chronicle an invaluable source for descriptions of politics in the early days of the Crusader States as well.

Raymond of Aguilers’ Historia Francorum: Raymond’s account is probably the least read of the major eyewitness accounts. Raymond was a priest, like Fulcher, and he was likely in the service of either Adhemar of le Puy (head Papal legate for the Crusade) or Raymond of Saint-Gilles (alternatively known as Raymond IV of Toulouse and Raymond I of Tripoli). In general, his account seems to side with Count Raymond’s political faction. Raymond of Aguilers’ account is most interesting for how he includes visions and accounts of miracles in his text. He gives an interesting perspective on the religious nature of the movement, and how that was represented in people’s actions and behaviour. He’s also the only chronicler to really concern himself with the poor commoners who also accompanied the Crusading army.

Peter Tudebode / Gesta Francorum: These are our 1.5 chronicles. Peter Tudebode was also a member of Raymond St. Gilles’ faction, and wrote his version of events in his Historia de Hierosolymitano itinere. The Gesta Francorum contains almost the exact same narrative as Peter Tudebode’s account, but written from the perspective of an Italian Norman affiliated with Bohemond (eventually of Antioch). There have been extensive debates about who the original author was (right now Tudebode seems to be the favourite) and/or whether they both copied from a third lost account. This account provides some of the most specific details of military practice (particularly in the Gesta version), and was very influential as many European chroniclers used it as the basis for their histories of the First Crusade, see for example Guibert of Nogent or Robert the Monk’s accounts.