I'll be referring to Case Closed as Detective Conan from now on, since I've been accustomed to calling it the latter.

Detective Conan is unique to me in the aspect that it has accompanied me on my anime journey from start to finish. Granted, it's still airing and hit 1000 episodes just a few weeks ago, (hooray!), but the fact that such a long-running anime has retained my attention really says something about it, don't you think?

Before I start, let me get a few things out of the way. Firstly, there will be minor spoilers from this point on. Second, I will include a Tl;DR at the very end for those who just want a quick-and-easy framework summary. Lastly, I haven't rewatched any older episodes save a few really good arcs, so my synopsis or certain references may be inaccurate. If that's the case, please let me know and I'll fix it.

Plot: Basically, a super intelligent detective, Kudo Shinichi, is attacked by the Black Organization after investigating a case and is given a drug that turned him into a child. He then continues to solve cases like the master detective he is under a new identity -- Edogawa Conan -- all the while meeting new people and getting closer to dismantling the Black Organization.

Although intriguing, the simple fact is that the plot moves at an incredibly slow pace.

The general episode format is: Approx. 50 episodes or so with a few character introductions/multi-episode cases sprinkled in, then a major plot/development arc, followed by another 50 episodes or so. Occasionally there will be re-runs or remastered episodes, but I'd say those are few and rare in between. If you're someone who wants a fast-paced anime, then this is probably now an anime you'll like. Patience is a necessity if you ever choose to watch Detective Conan.

Characters: There's a bunch. If you watch at a reasonable pace, you'll have no trouble remembering them all and their respective significance in the story, but if you really want to understand the whole plot, watch all of the anime or none of it. Characters are constantly added, so to stay on top of the game, one must also be up-to-date with the newest character developments.
Speaking of character development, there's also a bit of romance involved. Rare, perhaps, but it's there.

Trust me, it looks more intimidating than it really is.

Art: Given that this series started in 1996, I'd say it's a bit hard to compare the art consistency for all episodes. For me, there were three major art styles throughout the episodes. One is the retro and immediately nostalgic style in the first few hundred episodes. Then comes a slight change in quality and character design around the 400 to 500 ish mark, and finally, around episode 750 or so, the art starts looking clearer and more refined. Personally, I prefer the more clean look current episodes give, but don't expect crisp, clean, and contemporary-styled art from the get-go when starting this series.

Sound: I don't remember the OP and ED songs that much since there were literally so many of them, but the jazz OST is pretty damn good. Background music isn't really a problem, but after a while, you'll begin to remember them and be able to predict when they start playing.
Edit: I listened to like 4 hours of the OP's and realized I was completely wrong about all the openings being generic. Some definitely are, but others are distinct, like Butterfly Core.

Enjoyment: This is where review on shows like this have a massive downside, in my eyes. I absolutely enjoyed the living hell out of this show, but that's me. I know the high episode count inflated with hundreds of filler episodes may deter some people from watching it, but to be completely honest, I didn't mind the fillers.
If you do want to get a taste for what Detective Conan is all about but the 1000 episodes seems daunting (which it is), then perhaps start with the movies. They're not canon as far as I know, but at least you'll get a gauge of what the anime is like. However, if you plan to watch Detective Conan solely for the characters and plot, prepare to be greatly disappointed, since sitting through the episodes would be like watching paint dry for you. If you're just a casual watcher who loves some mystery though, I can almost guarantee you you'll love this anime. This show is more about a detective solving mysteries with a bit of plot development than a plot-driven story centered around a detective solving cases.

Case Closed.

TL;DR: Plot is slow, Characters are a bit above average, Art varies, Sound is generally good, but not a show for everyone. Make sure you have a strong determination to watch it all as well as an interest for crimes and detectives solving them.