Old baseball cards worth money are real, and age on its own is not what makes them so. What age does is change two probabilities in opposite directions: fewer were printed, and fewer survived in the condition buyers pay for. Whether a particular old card is worth anything depends on where those two land for that card.
Why older usually means scarcer
Print runs grew steadily through the twentieth century and then grew very sharply in the 1980s. A card from the 1950s or 1960s came out of a far smaller run than anything from the 1980s, and it was handled by children rather than stored by collectors. Both of those reduce the surviving population, which is the number that actually matters.
Why older also means rougher
The same handling that thinned the population also damaged what survived. Cards were carried in pockets, clipped to bicycles, written on and taped into albums. So the typical surviving old card is not sharp, and the price gap between a typical example and a well-preserved one at that age is much wider than it is for a modern card.
The 1980s cut-off, roughly
As a working filter, cards from before about 1980 are worth checking individually and cards from the late 1980s and early 1990s usually are not, because that period combined enormous production with careful storage. It is a filter rather than a rule: plenty of pre-1980 cards are common, and a few later cards are genuinely scarce.
Check one card properly rather than fifty roughly
Pick the best card in the box, identify it exactly, find five completed sales of it in a condition like yours, and run them through the checker. One careful reading will teach you more about what the rest of the box is worth than an afternoon of rough guesses, because it calibrates your eye against real prices.
Questions people ask about old baseball cards worth money
How old does a card have to be to be worth checking?
Before about 1980 as a starting point, and earlier is generally better. Treat it as where to look first rather than as a line separating valuable from worthless.
My old cards have creases and tape. Are they worthless?
Not necessarily worthless, but heavily discounted. For genuinely scarce early cards a damaged example can still sell, because some buyers want the card at any grade; for common ones, damage usually takes the price to nothing.
Should I clean or trim an old card?
No. Both are detectable, both destroy value, and trimming in particular is treated as alteration by graders and by buyers. Leave the card as it is.
Is an old card in a plastic holder already graded?
Not unless the holder is a sealed grader's slab with a certification number printed on it. A screwdown or a semi-rigid holder is storage, not grading.