I hate the term cartoon, as it's generally used to apply to any animated series and it's a term that definitely implies being targeted to children. That is not the case with all animated programs. Also the term cartoon definition began with humor being a major portion of it, which would apply all cartoons need to be humor fueled (or just heavily feature but that's not true of all animated programs either. It's definitely prevalent, but there are definitely exceptions even in western animation. Being a big fan of animation, much more than any other storytelling medium, I hate it when people apply that childish connotation to it. I understand why that happens, and don't get me wrong I do indulge in that stuff that does fit the description of cartoons (or at least, my definition of cartoon), but it's just a term I despise and wanted to get that off my chest.
Anyway, I'll be answering this question by looking through animated series, not cartoons. So everything, making it broad as hell. Growing up my favorite animated series without a doubt was Dragon Ball Z. Besides one about urinating in my own mouth, Dragon Ball Z is my earliest childhood memory. I still remember seeing the promos on Toonami, getting excited, and telling whoever was there that, "We have to see that." I remember one time where I had to rush through my meal because if I didn't finish, I wasn't going to be allowed to watch DBZ. Toonami and DBZ are my childhood and while I watched a ton of shows back then, to limit this just down to one, none stand above DBZ.
Today, well I look back on DBZ and it has more than a few flaws. Let's say that the Cell Arc (Future Trunks arrival to his departure more or less) was awesome and leave the rest out of it. I don't want to get into that on here again. As for my favorite today, I'll say it's a three-way tie between Bebop, Batman: The Animated Series, & Futurama. I often call Bebop 25 masterpieces and Boogie-Woogie Feng Shui (terrible, terrible episode) and I legitimately believe that. The amount of variety in the series is incredible, the animation still holds up today and even exceeds several shows (Especially Pierrot le Fou, holy crap Pierrot le Fou), and the OST is amazing. The variety and incorporation makes it one of the best out there, I'd say the second best (Wolf's Rain my favorite). Needless to say, the phrase, "I hate every anime except Cowboy Bebop" exists for a reason and that reason is because it's probably the most westernized anime out there, definitely of the ones I saw. JO said it best, "Cowboy Bebop is so much style over substance but still has better substance than 90% of other shows out there."
Sorry, I'll try and not fanboy as much for the other two. Batman: The Animated Series is incredible. While Bebop has several things over it, like OST, Batman still does pretty good with music at least in terms of incorporation (Perchance To Dream anyone). It doesn't present as much variety but it still has a good chunk, doesn't have an ending, has more bad episodes, and the last season is completely hit and miss (but when they hit, it's up there with the best . . . also Joker's redesign was awful). To put why Batman is on my list simply, when asked what my favorite episodes are, I was only able to limit it down to 26 episodes and that's with leaving some favorites off. I mean I eventually did make a top ten (well top eighteen, lots of toss-ups for the final spot) but still. Plus, it's the definitive Batman for me. Perfect casting for everyone. Also, Mask Of The Phantasm was a better movie than Knockin' On Heavens Door.
Finally, Futurama because sometimes I just want to laugh. Okay, it's not just that as both Batman & Bebop inject comedy in during certain episodes and both can make me laugh quite a bit (Almost Got 'Im & Toys In The Attic are the probably the prime examples respectively). On top of being really funny, Futurama also has a ton of heart (not trying to imply Bebop & Batman don't have this). Some of the episodes blend those things together perfectly. Luck Of The Fryish is one of my favorite episodes of anything ever. Other great episodes I really love that have said heart are Godfellas, Time Keeps On Slippin', The Sting, Jurassic Bark (though I think it's overrated), Leela's Homeworld & even one of the newer episodes in The Late Philip J. Fry. Futurama does have a lot more bad in it than the other two though.
Okay, I'm done gushing over the shows I love, hopefully I did them some justice. I probably could've added Wolf's Rain & Monster to that list but I tried to limit it down to three and I don't think anyone wants me to go on longer. In my defense, I spend most of my time on here bitching about WWE, so I kind of jump on the chance to talk about something I actually enjoy. I've also seen at least one episode of every show mentioned here, but I really don't want to make this post any longer than I already have so I'm just going to stop.