I haven't been alive long enough to have a good list. Give me another 30-40 years and hopefully I will...
C: Pudge Rodriguez, up there with Yadier as the elite defensive catcher of the past 20 years, and OPS+'ed at least 98 for 12 straight years in his prime. 98 is really solid for a catcher, and most of those years he was really much better - didn't walk much, but he hit .312 over that span and averaged just under 32 doubles and 20 HR in 129 games, great numbers for a guy who was simultaneously the best defensive catcher in the game, and one of the best ever. Also blew away the likes of Bench in terms of longevity.
1B: Albert Pujols, hands down. It's been a shame to see him decline so much at an age that feels very young coming right on the heels of the steroid era. One of the prettiest swings I've ever seen, and he still has it. Not hitting so badly this year, really...
2B: Roberto Alomar, such a dynamic player, did pretty much everything well, and played with a ton of passion. Chase Utley in his prime is a close 2nd. Cano is a great player, but for me he just lacks a little bit of that extra edge that put those 2 guys over the top. A shame that Utley also fell to the injury bug in his 30s and won't finish his career as a HOF'er; he certainly had the game to be one. This is the first time since his rookie season in 2003 that he's failed to slug .400. That's pretty darn good for a 2Bman. 11 straight seasons slugging .400+ and 5 of .500+ dwarf anything Morgan did.
SS: A-Rod. I'd love to take the career Oriole, but there's just no way that Ripken was as good as A-Rod. Sorry. I also always had a real soft spot for Rafael Furcal - every time I watched him play, he had a great game with the glove and the bat.
3B: A-Rod. Yeah, he makes the list at 2 positions. He's a great player. I guess you could also make an argument for Miggy here, but since he's grown into one of the best hitters in baseball he's been primarily a 1Bman, and frankly we all know he was well below average when he moved back to 3rd. If you do want a unique name here, I have one that I can't believe we haven't seen yet in this thread: Chipper Jones. No offense to Scott Rolen and his Gold Glove defense, or David Wright and his all around game, but Chipper could hit like very few other players in my lifetime. Head and shoulders above anybody else not named A-Rod.
LF: Mike Trout, the most dynamic player I've ever seen, and probably already moving towards competing with Pujols for the position of 2nd-best overall position player I've ever seen.
CF: Carlos Beltran. Objectively, maybe not one of the 3 best outfielders of the past 20-25 years, but as a young 5-tool player with the Royals and Astros he really blew me away. I'm also giving him the nod over Trout in CF; the fact that he never won a GG until he went to the Mets shows just how bad the GG voting system really is. For anyone who hadn't already started following him, he should have captured the imagination in that 2004 postseason in his one (partial) season in Houston. He went toe-to-toe with Pujols in the NLCS after carrying the team through the division series, I think he hit 4 HR in each series and batted close to .500. Just off the wall stuff, really only matched in my memory by Madison Bumgarner and this next guy.
RF: Bonds. Duh. Not really a RF, and if you want to switch him with Trout, be my guest. But anybody who leaves him off the list, no matter how old you are, is frankly being disingenuous. I don't care how hardline a stance you take against PEDs. The question was, who was the best player you've seen. If you've seen more than 2 OF more impressive than Bonds, you've got to be 100, because I can't think of any way to even argue for a group that doesn't include Cobb in his prime.
If we've got a DH, it's Frank Thomas. Really easy. He's Edgar Martinez + power, David Ortiz + longevity and a better hit tool, Baines + power, average, and walks,etc. Really just blows away the competition amongst full-time DHs, especially from a career perspective.
Bench: Manny Ramirez - where the hell has he been on these lists? He hit at least .300/.400/.600 6 times in his career. The only other players who can say that are Bonds, Ruth, Gehrig, Foxx, Williams, Greenberg, Hornsby, Pujols, and Musial.
Omar Vizquel - no offense to Ozzie, but Omar is my defensive SS. Less flash, more substance.
Jim Edmonds - Tough call who to add in the OF, and I realize Griffey is a more popular choice, but he never blew me away. I love Edmonds' defense.
Mike Piazza - Apologies to Yadier, but we've already got a great defensive catcher starting, and I'd rather have a guy who also has a ton of utility as a PH or backup 1B/DH on my bench. Mauer was also tempting.
Ben Zobrist - A bit of a stretch, as I wouldn't call him one of the best players I've seen, but he's a great utility guy to have on the bench. Michael Young was also tempting for this spot.
SP: Pedro, Maddux, Clemens, Johnson, Kershaw. I think all these names are fairly self-explanatory, and yes, they are in order.
With a DH and the bench 5 deep, I get a 6-man bullpen. Those guys are:
Long relief: Scott Shields; because of the quality of the rotation, we only need one middle inning guy, and this is the best one I've seen. He was badly overlooked.
LH Specialist: Jesse Orosco. I wanted to pick Steve Kline here, but I have to give Orosco some props for playing forever. I badly wanted to put Julio Franco on the bench and didn't, but I couldn't resist Orosco.
RH Specialist: Darren O'Day. I feel like a lot of people somehow don't realize how good he is. If you throw away his rookie season and his injury-marred, 16-inning 2011, the worst single-season ERA he's put up - in 6 seasons - is 2.28. The vast majority of those games were played for Texas and Baltimore, neither of which play in particularly pitcher-friendly home parks.
Setup: Craig Kimbrel, apologies to Trevor Hoffman. I've never seen any other pitcher dominate for multiple seasons the way Kimbrel did. Just untouchable.
Setup: Billy Wagner. We ought to have another lefty in this 'pen, so I'm adding the best one ever to throw a baseball. I'd love to have Aroldis Chapman and his massive firepower, but this isn't about the most intimidating pitcher or the greatest K artist. It's about the greatest player. That's Wagner.
Closer: Mariano. Duh. There were a couple of guys who listed somebody else. I don't care how you feel about the Yankees... as with Bonds, it doesn't even matter how old you are, if you didn't pick Mariano, you're not being entirely honest with yourself. You've never seen a better closer than this. Maybe for a few years Eck came close, but in the end, nobody touches Mo.