Hmm...I think there have been a few Anime with "normal" characters. "Here Is Greenwood" or whatever is what I'd consider a good Anime even though it is full of "normal" people. I haven't seen it yet but "Piano" is another one that seems like it is full of "normal" characters. I think it's easy to forget sometimes that Anime / Manga has something for everyone , not everything is Mech ...Hentai..."Crazy"...ect. There's some series that have a focus on ice skating and romance , fashion , cooking , ect. Although when we think of "ren'ai" , we do tend to immediately think of games , there are also ren'ai Anime and Manga series.
Even though series like Ranma and the anime version of Princess Maker ( petit princess or something like that...I don't know why they didn't want the anime to have the same name as the game series ) can and do have lots of fantastical stuff going on in them , I would count them as ren'ai series too. Ranma has to deal with many people either "promised" to him in one way or another...The main girl in Princess Maker always falls in love with the prince or whatever....
I agree that "normal" doesn't nessicarily mean "boring" or "shallow".
Sometimes you may want to take a break from all the regular "crazy" stuff and watch an Anime with "normal" people in it. I think something like that would by why anyone would want to put "normal" people in their Anime or make an Anime that's a "normal" kind of life. Even though I focus on fantasy most of the time , I also like to make "normal" characters with "normal" lives / stories. As for "normal" people falling for "normal" people...I think that's not always true. I was struggling for a good example but just now I thought of Princess Diane. Wasn't she a "normal" person who fell in love with a prince? I think , even for modern day princes , alot of people look up to these people / think of them as living legends. So , in that way , they are not "normal".... But if they watch the news and stuff , the illusion is shattered , so people have to deal with the fact that the people they've admired so much are in fact not that different from them. You know what I mean?
Sorry for any bad spelling.
BTW I haven't seen any / most of these but these are titles I'm either interested in or have found while looking for examples.
I've seen some of "Here Is Greenwood" though.
Whisper of the Heart
Take away the fantastic from certain series and what you're left with is a "normal" story with "normal" characters. : Junkers Come Here , Hikari No Go ( or just "Go!" / "Go" as some people refer to it )
http://piano.rightstuf.com/
http://www.sleepisfortheweak.org/articl ... houjo.html
( I don't agree with some of the things stated in the article but otherwise and overall it looks to be a good read. )
http://boys-be.rightstuf.com/
http://www.shonenjump.com/
http://gravitation.rightstuf.com/
http://niko-niko.net/random/contents.html
http://comicparty.rightstuf.com/
Only Yesterday
Golden Boy - "student of life"...one man...many women...funny situations...blah blah blah...
Marmalade Boy - what their parents decide to do is weird and things only get weirder when they realize that they've fallen in love with each other...the "normal" parts of the story...struggling with parental decisions, falling in love and growing up , new brother / stepbrother...blah blah blah.
Junk Boy - horndog looking for a job , especially one where he can be surrounded by beautiful women on a daily basis
My Neighbors the Yamadas
Wow , actually the list can go on and on...just like anything , you just have to know where to look for them and keep an eye out for these type of stories.