In our previous posts we discussed the difference between an ox classified as a tam, a domesticated animal who is not at risk of attacking others and a muad an animal that has a history of attacking others. Such a classification exists only by animals. Regarding humans no such distinction exists because humans are always classified as muad whether "by accident, intentionally, whether awake or asleep" (Bava Kamma 26a) and must always pay nezek shalem, full damages. First offences, accidents, even sleep does not exempt one from the full consequences of one's actions. As higher functioning animals, homo-sapiens have an obligation to take every and all precautions necessary to prevent damage and even our best may not be good enough. While we may be partially exempt for damages caused by our animals, direct damage we may cause has no such dispensation. When our actions cause a loss to an innocent party we must pay, period [1]. 
What makes this most instructive is that such is true only in regards to financial damages caused to another. One who accidentally, and surely one who in his sleep, violates Shabbat is not held liable. The halacha specifically requires melechet machshevet a conscious intentional act, regarding Shabbat. Similarly even the institution of galut, of sending those who kill accidently to a city of refuge requires intent to act, if not intent to kill. However one who accidentally trips and falls another killing him would be exempt from exile. There are accidents and there are accidents. Chopping wood and having the handle (or piece of wood) go flying and accidentally kill someone is not the same as slipping on a banana peel and by awful fluke falling on someone and killing them. 
That people are generally not as careful as they should be serves as an explanation for the second category of damages, that of bor. The classic case involves digging a pit in a public causing injuries to one who falls in but extends to other cases where a (stationery) object is left in the public square causing damage to a passerby. It is such a scenario that serves as the opening to the third chapter of Bava Kamma.
The Mishna (Bava Kamma 27a) begins by exempting from and assigning liability to in the case where one leaves a barrel in a public area. If a passerby breaks it as he is walking by he is exempt from paying for any damages caused to the barrel. Furthermore if the barrel injures the passerby the owner of the barrel must compensate him for his injuries. 
This ruling troubled the Gemara. The Gemara, working on the reasonable assumption that one should watch where one walks, wonders why the Mishna does not rule in the exact opposite fashion. Should not the passerby be held responsible for any damages he causes? If there is a barrel in the street walk around it! As Tosafot so powerfully explains "yoter yesh lo lishmor shelo yazeek meshelo yuzak, one must be more careful not to damage others than to be damaged oneself.[2]" (Tosafot Bava Kamma 27b s.v. Amai)
The Gemara gives a series of answers explaining why this case is different. Rav explains that the street is full of "barrels" making avoiding such impossible and hence the barrel owner liable. Rav's colleague Shmuel explains that under normal circumstances it is one's responsibility to watch where one is going but the Mishna is referring to a case at night where one cannot see what may lay on the street and as such liability shifts to the barrel owner. 
Rav Yochanan has a similar approach explaining that the ruling of the Mishna is limited to a case where the barrels are placed in places where they are hard to see such as just round a corner or at an entrance way to a courtyard. 
The above reasons all agree that it is the one walking on the street who is generally responsible for damages he causes but explain why the case of our Mishna is different. Ulla has a fundamentally different approach, one that exempts the passerby from responsibility for damages he may "cause". He argues - and it is his view that the halacha accepts - that "it is not the way of people to be careful on the streets." (Bava Kamma 27b) When we take a stroll we should be able to expect the streets to be nice and smooth without objects strewn about. One has no right to leave something in the street even if people could in theory easily avoid it. 
Yet at the same time it is not always smart to insist on being right. Precisely because man is "muad leolam", is a creature who is constantly at risk at causing damage that even if one not legally need to watch where one is going one ought to do so.  
[1] Tosafot (Bava Kamma 27b s.v. Shmuel) claims that if it ones gamur, an accident totally beyond one's control one would be exempt a view disputed by others.
[2] While one can use that same argument regarding the owner of the barrel it appears that the damage he causes is more indirect as opposed to the one actually walking the streets. If you have a better suggestion I would love to hear it.