I've got a lot of coins I love, but these are 4 of my favorites:
1. My all-time favorite coin is the 1955 doubled die cent. I've wanted one since I started collecting coins as a young teen in the 80s. I bought this one at a good time, right before it's last big price jump. I bought it as a raw XF on eBay for about $700 (which I prob wouldn't recommend cuz there are so many fakes out there). I sent it to PCGS when I was in their collectors club with about 4 or 5 other coins. It came back AU50. Current PCGS price guide lists it for $1825!
2. My favorite series is the Morgan silver dollar. A few years ago, I started to put together a full set. I took the advice of the old timers and have been acquiring the key dates first. (This way, you can buy the expensive coins before they go up in price so high that you can't afford them.) I sold the bulk of my silver stash from coin roll hunting to pay for a family trip to Europe and this nice mid-grade 1893 S. I'm glad I did, because with kids getting close to college, etc, I will probably never have a chance again to get one. I now have the big three: 1893 S, 1889 CC, and 1894, along with several semi-key S-mints and O-mints.
3. Another coin I love is a 1921 S Buffalo nickel. It's not near as valuable as the other two mentioned, but is special because it was a gift from my brother and because he found it in circulation. He pulled it from a roll in the cash register at work and have it to me cuz he knows I live coins. I have found a few dozen Buffs from rolls over the years, including a better date '18 D, but the odds of finding a '21 S, one of the lowest mintage nickels (even back in the 40s and 50s when they still circulated) is nearly impossible. If it weren't for a small scratch on the obverse, it would probably grade F12, and be a $150ish coin.
4. Lastly, I've added an 1808/7 half dollar to the list. It's not particularly valuable either, but it's my oldest coin and a gift from my father in law, who's a great guy and gave it to me as a gift. Along with this coin, he filled a Dansco Type coin album with several other coins from his collection and gave them to me for Christmas one year. I sent it in for a free grading I had as a PCGS collectors club member (knowing it would get a low grade, but it was free and I didn't have anything else to submit at the time). It is a pop 1/276 coin, the lowest graded for the date (for any of you lowball set collectors out there).
Anyway, there you have it.