As I said in the title, I'm looking for some old dramas that have an interesting plot or a good chemestry between the characters. I've noticed that most of the dramas I've seen appeared only in the last few years and I'm sure there are many other great dramas out there that are worth watching, despite their old airing date. So, if you know any old dramas that are pretty good, please let me know :)


Edit: By old dramas I mean everything that appeared before 2008, not necessarily in the '90s
I haven't seen that many older K-dramas, but the few I did see were mindbogglingly makjang, poor production values, poor acting, poor scripts. It's not that the picture and scenery were merely old fashioned, the overall quality of their productions just was not good. On the other hand, many Japanese oldies are golden.

Here are some that I liked and rated at least 7 and above. Some of these dramas will have sad or crappy endings. Sad meaning someone dies at the end and crappy meaning the drama is great up to a certain point (usually up to last 2-3 episodes) then takes a complete and unexpected plunge into left field. Some of these dramas would have been rated higher if they had better endings, esp those in the latter group.

Aishiteru to Ittekure (1995)
Mahiru no Tsuki (1996)
Oishii Kankei (1996)
Cheap Love (1999)
Ice World (1999)
Beautiful Life (2000) 

Others I found problematic, but will mention anyway since I don't know your taste. Just maybe you might end up liking them a lot more than I did.

Imoto Yo (1994)
For You (1995)
Meguri Ai (1998)
Love Story in Havard (2004)

P.S. Some of these dramas can be found on popular streaming sites, others you can download from avistaz.to. Hulu has a few too, the last time I checked.
LoL … With your long PTW list, you still want more recommendations?  But I understand … newer dramas after a while it's like "You've seen one, you've seen them all"  or  midway through the drama, it starts to drag.

As Member PrettyCarEye mentioned, Japanese dramas back in the "old days" were well-done.  The problem is trying to find them now.  That's why my recommendations here are K-dramas produced over 10 years ago but still easy to find (#2 and #3 are already on your PTW).

Honesty (2000) -- interesting story and "marathon-worthy"
Sorry I Love You (2004) -- sad but oh what a beautiful love story -- great chemistry between the Leads
My Girl (2005) -- very entertaining and great chemistry between the Leads
I'm currently watching Kimi no Te ga Sasayaite Iru (from 1997). If you like slice of life/family dramas then you can give this one a go. 
I'm hoping this will be a golden oldie :) 
(If you need d/load links you can send me a PM, older J-dramas with subs are harder to find).
Up to what year do people class old? 10 years?

My highest rated (9.5-10) oldies are City Hall (2009). Also Smile, you (2009), J and T Hana Kimi (2007/6), Nodame Cantabile (2006), Wonderful Life (2005), J Liar Game (2007), Hana Yori Dango (2005), T it started with a kiss (2005), Full House (2004), Sweet 18 (2004), My girl (2005) and Pride (2004).
Agree with what PrettyCarEye said. I'll add some recommendations:

Tokyo Love Story: This is one of the Jdrama classics. It's popular, and seems to be liked by many, so you might want to check it out.
Lunch Queen: More of a food/family drama (if I can call it that), but there's a romance in it, and the leading lady does have an excellent chemistry with at least two male characters.
Ruler of Your Own World: This drama has so many melodramatic elements rife in early 2000s dramas (fatal disease, social disparity between the leads, dark past, birth secret, love square). But somehow, those elements fit seamlessly into the story that they just felt natural, not cliched. I love the leads because they are so nice and honest to each other, and the acting is superb, too.
Thank you a lot for your recommendations! And I know I have a very looong PTW list, but I have the bad habit of adding every drama I come across on that list and it's so big now, I don't even look at it anymore xD That's why I ask people for recommendations and it also helps me when I want to watch a certain type of drama, like in this case.
Trick- It's a Japanese drama from 2000. About a female magician helping a professor disprove psychics. It's a comedy with some really good mystery elements.
Love Story in Havard (2004), For You (1995)
Here are my favorites from before 2008:
(all are J-dramas unless otherwise noted with a * which is a K-drama)

Galileo (2007)
Yama Onna Kabe Onna (2007)
9 End 2 Outs* (2007)
Dal Ja's Spring* (2007)
Dare Yori mo Mama wo Aisu (2006)
Galcir (i.e. Gal Circle) (2006)
Jikou Keisatsu (2006)
My Boss, My Hero (2006)
Sapuri (a.k.a. Suppli) (2006)
Yaoh - King of the Night (2006)
What's Up Fox?* (2006)
Couple or Trouble* (2006)
Engine (2005)
Nobuta wo Produce (2005)
Tiger & Dragon (2005)
Last Christmas (2004)
Ms. Kim's Million Dollar Quest* (2004)
Kimi wa Petto (2003)
Koi wa Tatakai! (a.k.a. Love or Fight) (2003)
Manhattan Love Story (2003)
Stand Up!! (2003)
Water Boys (2003)
Kisarazu Cat's Eye (2002)
Satorare (2002)
GTO (1998)
Beach Boys (1997)
Gift (1997)
Virgin Road (1997)
Long Vacation (1996)

 
...Iwyn I see you've already seen some of these and since you enjoyed GTO so much maybe I would specifically point out Sorimachi Takashi's other 90s dramas**, Virgin Road and Beach Boys? One is a romance and one is a bromance and they're both so enjoyable (I seriously wish Sorimachi Takashi still did romantic comedies still, he's so charming).

(** I did not include Over Time because, although I liked it, the ending was disappointing).
2007 was a fantastic year for K-dramas - not all of these are romantic, but some of my favorites that aired partly or entirely that year include Capital Scandal (part romantic comedy, part anti-Japanese occupation resistance story), Evasive Inquiry Agency (a wonderful, funny, touching show - hard to summarize but very unique - the production values aren't great at first, but stick with it as it gets better and better), The Devil (a dark, smart, and ultimately incredibly moving thriller) and Jumong (a huge epic historical with fabulous production values - tons of fun if you don't mind the length). Conspiracy in the Court and Time between Dog and Wolf are also really interesting although I found that both of them had underwhelming endings.
@PrettyCarEye - I understand that many of the old productions have a poor background, but as long as I will be able to enjoy a nice, pleasant story, I'll usually just overlook this fact. I love j-dramas, so I'm really interested in your recommendations~ there are so many that caught my attention, so thank you! :)

@shiu545 - I actually wondered for a long time if I should start watching them, so I might finally give them a chance xD

@winnie, @squeakyelle, @oyaji - I've never heard of them, so thank you a lot!

@oppalover87 - Wow, these are like all the dramas that I keep putting off and they're very appreciated too, so I should start watching them some time soon!

@kittyflumpin - I love your recommendations! I have already watched some of them and I really enjoyed them, so I'm sure I will like the others too. And yeah, I really love dramas like GTO, so thanks for pointing out those 2 other dramas :D

@wonhwa - I don't think I've watched any drama that aired in 2007, so your recommendations are very welcomed~ thank you a lot!
Some older Dramas I'd recommend that I really enjoyed. Mostly Japanese ones & a few Taiwanese ones. I only glossed over what others recommended so I might have added a bunch that have already been recommended. Hopefully there's something in there that looks interesting to you. 

Long Vacation
Beach Boys. This is great if you want something relaxing & easy with a good male friendship.
Ikebukuro West Gate Park
Yasha
Strawberry on the Shortcake. Can be quite dark but the ending will surprise you.
Long Love Letter. Unique sci-fi-ish.
Boku Dake no Madonna
Orange Days
H2
Tokyo Friends
Engine
Hana Yori Dango. Mix of comedy & romance. Pretty easy on the eyes. 2 series + a movie, so will keep you going for a while.
Brother Beat. Pretty decent family Drama.
Slow Dance. More serious adult romance.
Tatta Hitotsu no Koi. I remember the first episode being a little draggy but totaly worth it after that.
Hana Kimi. Simple & easy on the brain.
Innocent Love. I'd recommend this if you enjoyed Last Friends & vice versa.
Last Friends. Great serious Drama with youthful but good actors. 
Koizora. Quite sad.
Maou.
Ryusei no Kizuna
Cat Street
RH Plus. This is a little cheesy but if you like Vampire stuff it's still pretty good.
Akai Ito. Like a younger version of Last Friends, pretty serious themes.
First Kiss

The Rose
MARS
Devil Beside You
Why Why Love

(Edit: Added a tiny bit of info for some of the suggestions which may help when picking something, depending on your mood.)
'Que Sera Sera' is really good with great chemistry between the couple. 
Thanks @Pantheria! There's a lot to choose from ^^

@lunatepe - Many people recommended me that drama, so I'll definitely watch it soon!