Today, as well as in ancient times, it depends on where you are.
A grave example is Romania. Under Ceaucescu the country underwent a forced industrialization that resulted in people flooding the cities. To make room they tore down houses and built high-rises. But as apartments (generally) was small etc. dogs were left on the streets where they was left to breed. Today it is close to an epidemic.
There are also a lot of other places around the world that has similar issues. Wild dogs, and half-wild etc. are generally sick ridden, full of flees, can be really dangerous, etc.
From what I have read one had the same issues back in the day. Dogs roamed around outside (and surely inside) the cities. (They licked the wounds of Lazarus.)
And let's face it. Dogs are scavengers as well as predators. There are even several passages where dogs eat the flesh of man.
They also kept domesticated dogs as we for example read in Job (one of the oldest books):
Job 30:1: But now they that are younger than I have me in derision, whose fathers I would have disdained to have set with the dogs of my flock. (sheepdogs.)
In Mark we are presented with a verse that tells us dogs were also allowed in house (pets?):
Mark 7:28: And she answered and said unto him, Yes, Lord: yet the dogs under the table eat of the children's crumbs.
Dogs are lovely animals, but they can surely also be grim. Especially dogs that are not domesticated living from trash, carcasses, etc. There is also a reason we have expressions like dog-fights etc.
Even today it is common to use dogs as a way of low word. Bitch and "dog of a man".
Actually the word dog in GT has (mostly?) the strongs definition:
3611 keleb keh'-leb
from an unused root means. to yelp, or else to attack; a dog;
hence (by euphemism) a male prostitute:--dog.
Not the most positive one.
At the same time the Hebrew word for dog is "kelev" and from what I have read Caleb (with Moses) actually comes from "dog". We know Caleb was faithful, has a big heart etc. but if this has any linkage is pure speculation on my part. The 16th century rabbi Maharal wrote that a dog is called "kelev" in Hebrew as it comes from "“k’lev," which means "like the heart" ... ;)
The first passage I can find is Exodus 11:7
But against any of the children of Israel shall not a dog move his tongue, against man or beast: that ye may know how that the Lord doth put a difference between the Egyptians and Israel.
As such it is worth mentioning Egypt. Dogs was wholly for the Egyptians and the Abuwtiyuw is one of the earliest documented domesticated animals we know of. It is believed to have been a guard dog. There are also paintings like this one:
Generally dogs were used both as guard dogs, hunting dogs etc. in Egypt.
Find it difficult to say anything concrete about how dogs was used beyond as sheepdogs and (perhaps) some kind of house dog, but the verses about "throwing meat to the dogs" indicate that they might had dogs around beyond sheepdogs. If so the case of giving them unclean meat would also mean they acted like disposal animals. If not they would have had to get rid of unclean meat by other means.
Even though the word "dog" often are used in a negative setting the overall treatment of animals is very strict in the Bible. One shall treat them with respect and work animals are to be allowed to rest on Sabbath etc. In general: respect for the creation.
You might find this interesting:
Small addendum. Not that much on species. Have not found any good source on that topic, but came across this paper while searching that I guess you find interesting:
Geoffrey David Miller, Attitudes toward Dogs in Ancient Israel: A reassessment
The article also list quite a few resources that might shed some light on the topic of species.