Wow stereotyping much?
there is no definition of a rival that indicates it has to be an enemy. A rival is just someone striving for the same goal as you are, an opponent mind you.
ri·val

/ˈraɪ

vəl/

Show Spelled [rahy-vuh

l] noun, adjective, verb, -valed, -val·ing or ( especially British

) -valled, -val·ling.
–noun 1. a person who is competing for the same object or goal as another, or who tries to equal or outdo another; competitor.
2. a person or thing that is in a position to dispute another's preeminence or superiority: a stadium without a rival.
3. Obsolete . a companion in duty.
- Dictionary.com
The majority of Ash's battles in the anime are friendly; he wants to be the master yes but at the same time he is always making friends with the other trainers he meets.
I found it refreshing that the Pearl/Diamond rival was your childhood friend, and then having two best friend rivals in Black was even better, especially with their completely opposite skill levels. Bianca was especially refreshing because she accepted without complaint that she just couldn't manage to be a strong trainer. It's healthy and responsible to know what you are capable of and what you are not, know your limitations as they say right? She even found a way to use what skill she did have being body guard to the Junipers.
Then Cheran was interesting too, being your basic combination of both Gary and Silver with a drive to outshine you like Gary and to be the strongest trainer like Silver but then an new addition of friendliness. He was also the first rival to be questioned and made to wonder what being the strongest trainer really meant to him and what he would do with such a title.
If I remember correctly because it's been years, in the anime Gary felt he needed to prove himself to Oak, his grandfather. His goal was not only to be a strong trainer but to see every pokemon with quite a bit of narcissism in him characterized by all his cheerleaders. In the game it was still there in the form of always bragging about himself whenever he would approach you. The very first time you see him after the beginning in Cerulean he immediately starts telling you how many pokemon he has already caught.
"I've already seen 40 different kinds of strong and smart pokemon"
(or the line is something like that).
This says he also values his team. To Gary being the best was all about his narcissism.
Silver on the other hand was a heartless jerk, his desire was not necessarily to be better than you but rather to get rid of you. He viewed you as pretty much just this show off pest, when really he is clearly trying to be the show off. He has no respect for his pokemon, his only concern is that they are strong and can wipe out anyone in his path. He was destructive; like a vampire everyone was pray. In a way he had an attitude similar to N in that he had a blind view of the world, unable to understand what pokemon truly stood for and what they meant to humans as well as vise versa. He was not striving for the same goal you were, so you could say Silver was not actually a rival. He did not care about the pokemon league, he only wanted to show others how weak they were. You see it from several characters you encounter in every generation of the games, the hero is about having the best bond with pokemon anyone has ever seen and that is how you end up at the top. To me Silver seemed more of a nemesis although he did not need to be stopped from doing anything but rather taught better.
Now May and Brendon(in my case May as I am always Brendan), as far as I can see they actually have absolutely no point. So they are the professor's kid and help with some research, not only are they weak despite being implied to have been successful trainers long before your beginning but they are quitters. After you battle them in lilycove they suddenly wanna go home to daddy...oook? Clearly there is no shared goal there, so I would not much call them rivals either.
Wally on the other hand is a bit like Charen in that they are both friendly and strive to outshine you, and on top of that he was something of an underdog. I believe it's said that he begins as a sickly boy who is very naive about the world of pokemon trainers(at one point begging an uncle to challenge a gym after not having spent all that much time with his first pokemon). You don't see much of him throughout the game, only battling him twice that I know of, but he definitely has the drive of Gary and Charen with the friendliness of Ash kind of. I liked him a lot and wish he was more of a recurring rival than May and Brendan.
Gary, Wally and Cheran I think are the best examples of rivals; they all have a great drive to be the best while liking what they do and having respect for their pokemon. Gary is a show off and a bully while Wally and Cheran are friendly which is a great verity of the same goals and drive but different ways of viewing their rivals and approaching it. A perfect example of how some rivals can be jerks but not all
have to be to have drive and ambition.