I looked up what that saying means, and it said that back in the late 1800's single cents had significant worth and were the favorite target of counterfeiters. People would typically find fake or "bad" pennies in with their pocket change and would have to slip them by shopowners to get rid of them. It wasn't unusual to see the same one come back to them, so the phrase became popular.
Aside from horribly damaged or designed cards, or those of players I can't stand, I've never actually seen a "bad" card. But these are cards that somehow have much greater odds of ending up in that random mixed pile of (in this case 1970's) Topps cards. They're always in everyone's dupes box.
I disqualified any of my numerous player collections, because I always notice those. Also, I didn't elect those with actual cool looking cards, or most error cards that have corrected versions, because they are more sought after too. I won't call them "bad" players, but I guess I define a "Bad Penny" card as the most common commons.
I sifted through a couple Donruss sets from the early 80's but I really didn't find any examples in those sets, probably because I bought them as whole sets when they came out, so I didn't have to look for singles. So my candidates are from Topps sets of the 70's and early 80's.
Each collector will have his or her own examples for any given set. Here are mine:
1980 Topps - #563 Will McEnaney
I'm not even sure how to pronounce his last name, but Will is the one card that sticks in my mind for this concept. I've seen him everywhere. Don't even think he has too many other cards. Quick check of the TCDB shows that his rookie is 1975 with the Reds, continuing in '76 and '77, and he also had single Topps cards with the Expos and Cardinals, though his '77 OPC is with the Expos.
Runner-up: #385 Enos Cabell
1979 Topps #403 Tim Foli
Runners-Up: #21 Kevin Kobel, #304 Swisher, #438 Horace Speed
1978 Topps #520 Larry Hisle
1974, 1977, and 1979 Topps, he's having a much batter time there. Like I said, not a "bad" card, just see it a lot. Larry would otherwise be in the top 20-ish of guys with the coolest "card careers". Someone has a series on card careers, but I can't find it right now.
Runners-Up: #151 Milt Wilcox, #178 Dave Chalk, #517 Andres Mora
1977 Topps #436 Turn Back The Clock - Bob Keegan
Minnie Minoso's Record Breaker too, but I like him too much to put him in this list. One-(no)-hit wonder Bob comes out the winner for '77.
Runners-Up: #232 Minoso RB, #474 Rookies, #651 Von Joshua
1976 Topps #258 Nyls Nyman
Lerrin LaGrow, who I almost collected at one point back in the day when qualifying as a player collection meant you were somewhat interesting and I had more than three of your cards. Nyls (rhymes with gills or styles?) basically has a '75 quad-player rookie, this '76 Topps, and he made the big SSPC set. But he makes this list.
Runners-Up: #6 Stennett RB, #138 LaGrow, #268 Del Unser, #345 Andy Messersmith
1975 Topps #575 Gene Clines
DeMolas in my dupes box, but that one is cool for the colors and the ads behind him. Wanted to say Milbourne, but ya can't put up the Rookie Cup guy, especially in matching red and yellow. And Nate Colbert is just way too happy!
Runners-Up: #391 Don DeMola, #512 Larry Milbourne, #599 Nate Colbert
1974 Topps #577 Mike Sadek
Sadek wins for his genericness. He has minimal cardage, consisting of regular Topps cards until 1981, plus a Donruss in that year. He ended up coaching for SF and got a Mother Cookies coach group card.
Runners-Up: #170 Melton, #375 Williams, #496T Tom Murphy Traded
1973 Topps #364 Rick Wise
much longer career as both player and coach. His cards go from a 1964 dual rookie, through 1982, and then from 1985 to 2009 coaching in the minors. Good player, just cheesy common card. And like Sadek, he beat Roric Harrison (again with the Orioles), Lee May (Astros), and happy George Hendrick. Before this year, I would have said Roy White hands down, but I got his auto this past National. He's kinda the same deal as Wise - decent player with a card that doesn't go away.
I figure I'll stop here. Not just because it's 1 AM, but from 1971 and '72, the cheese factor diminishes greatly since those sets are so cool to start with. And I'm not finished 1970 (or '72), so I can't say I've done all the sifting for those yet.
Maybe I'll make this a series and do the 80's next.... Let me know what your nominees are.