The Mystery Cartoon Character Game, ongoing-ier.

Ok, I was able to put a character together.

I started out in a field, and ended up at a subway station.
I was found by a boy who took care of me.
My new friend has an unusual best friend.

Well, I can rule out one who's already on the list. Can't think of any others who match the clues.

Okay, because of thirteen-day, I never checked in to recognize Lucky Seven Sampson from Schoolhouse Rock. "Well, Lucky Seven Sampson is my natural name / And if you should ask me again, I'd have to tell you the same." Such a cute li'l boingy bunny from the cabbage truck that visits the city and delights the kids. So I'm thinking this is another Schoolhouse Rock character, and the subway clue points to the funk tune "I Got Six" and the unflappable black kid with six balloons. So: the Got Six Kid, for the win.

Nope, not Got Six Kid. I actually never seen that one.

Chester C. Cricket (I think his middle initial is C.) from "The Cricket in Times Square."

You got it FluidGirl, it's Chester!

He was out in a field and hopped into a picnic basket. The owner picked up the basket and brought it into the city.
Chester ended up in the subway where he was found by a boy.
His new friend is a mouse, whose best friend is a cat.

Wow, I'm on a roll! Of course, saying that, I probably jinxed it. Anyway, here's my latest:

1. Music and espionage are my life
2. My team gets our orders from my instrument
3. I'm always ready to spring into action

Ah, simple as pie. It's Coil Man, from "The Impossibles."

1, Self-explanatory.

2. Big D contacts them via a miniscreen in Coily's guitar.

3. Self-explanatory again.

You got it, Em. Your turn again.

Thanks, Fluidgirl. Now for one who isn't very old:

1. I'm the villain of a recent Oscar and Golden Globe winning animated film.

2. I fake my death in a fire that kills the protagonist's brother.

3. My last name clearly indicates Irish ancestry.

Ah, this is simple! This is Professor Robert Callaghan-aka Yokai from Big Hero 6.
Funny part is, I was actually spot on at guessing who the man behind the mask was when I saw it in the movie theater with my boyfriend--who despite his comic book knowledge and ability to figure out plot twists actually did not see this one coming. I just didn't think it was going to be so simple as to be Alistar Krei--so I thought who else could it be? Tadashi was clearly gone, and far too nice a guy to end up being the villain (Although before the film came out in theaters, I thought it would be a neat plot twist.) so I figured--hey, Callaghan could have faked his death.

Good job, Glowworm. All clues are self-explanatory, so you get to go again.

Thank you. Here's a good one.
1. I take part in a parody of a well known police detective.
2. I am part of the rogues' gallery.
3. I sneak up on the protagonist near the end of the short, but am turned into an advertisement.

I know this, but I'll wait a bit and see if someone else gets it.

Oh, what the heck. I'll answer. It's Neon Noodle from "The Great Piggy Bank Robbery."

1. The short is a parody of Dick Tracy, in which Daffy dreams about being, who else, Duck Tracy.

2. Neon Noodle is part of a rogues' gallery, each of whom is a spoof of some Tracy villain.

3. When defeated, this baddie becomes a sign that reads "Eat At Joe's."

*smacks self in head* This is usually my issue. I don't know such an obvious character until someone else gets it.

Correct, Emeraldisle. It is Neon Noodle from "The Great Piggy Bank Robbery"

Thanks, Glowworm. Now here's another I held back on for quite a while:

1. The tale of me, my family, and my precious cargo has been animated many times.

2. By coincidence, one of my voice actors famously played a rancher who had three sons just like I did.

3. According to a classic song traditionally played on St. Patrick's Day, I gave up on some mythical beasts, and left them behind to perish.

This must be old Noah, from the Great Stories From The Bible series. The actor you reference is surely Lorne Greene from the Bonanza western series. I haven't seen this one yet, but speculating from a single-panel cartoon, it seems that unicorns got left behind somehow when the floodwaters began rising. The comic panel showed the ark drifting toward the horizon, while two unicorns watch it. Their wet hooves indicate that dry land is about to become horribly scarce, and the male unicorn grouses at the female: "It couldn't wait until we got on board?"

OUB, you nailed it. It is he. And BTW, the song, of course is "The Unicorn" by the Irish Rovers. So step up and take your well-deserved turn on this lovely Irish holiday. Great job.