Hello :D

I'm looking for dramas where the main guy - just some ordinary guy - falls in love with the female lead (she may fall for him too, but I don't mind if she doesn't), and then they got separated. Years pass and the main guy meets the girl again (and very important - he recognizes her!), but this time he's rich and successful (he might be an actor, CO, whatever). He fights for her, of course, and is pretty jealous of every guy, because he was the first who felt for the girl ;)

Fox examples: My Love Eun Dong, Cunning Single Lady, Discovery of Romance.

Similar dramas: EXO Next Door (I guess, but he doesn't recognize her...), City Hunter (well, he does know her and love her even before they meet :P).

Will it Snow at Christmas? (Though I cannot remember what the male lead does for a living when they meet again so I don't know if he's rich or anything, but I don't think he's famous)
I Hear your voice 

There are many dramas where the two leads meet again but the male lead doesn't remember her, so I left them out, I think these are the two dramas I remembered that could best fit your description :) 
I've seen 9 eps of "I Hear You Voice" and the main guy isn't rich or succesful... he's just a high school student and I'm not into noona romance, so I dropped it :(
But I'll try with "Till it Snow for Christmas?" :) thanks :)
Well, My Sunshine sounds just about right. I didn't like this drama one bit, but you might so have a look/see for yourself.
As close as it gets... Try these ( couples get separated and reconcile again) 
EMERGENCY COUPLE (divorce and dating again) 
SAY I DO AGAIN / Say Again Yes I Do (separation) 
CAN'T LOSE (couple on bridge of divorce) 
UNEMPLOYED ROMANCE 
ANGEL EYES
I enjoyed watching Paradise Ranch, it's quite similar to what your looking for plus it has a cute ending. https://en.wikipedia.org/wiki/Paradise_Ranch  
Wonderful Days, but there is no love triangle
May Queen
I second "Will It Snow for Christmas?"

"I Hear Your Voice" is great too, but the guy is not rich.

Then, I'm not really sure because I watched it long time ago so I don't really remember the story, but somehow "Spring Waltz" also pop up in my mind.

Lastly, "18 vs. 29". It might be not exactly match with your description; they are married but the girl lost her memory. She only remember that she hated the guy when she was in high school.
I second My sunshine, I got hooked watching it :P
Also what you've asked for is pretty much the plot for When I see you again, it's airing at the moment so you wont be able to watch all the episodes yet.
Hi My Sweetheart, pretty old drama though. Ring Ring Bell also seems to fit your description.