Depends on what set they're from and what they are. For example, Unlimited was the last white border set to contain "Power Nine" cards like Black Lotus, the five Mox cards, Ancestral Recall, Time Walk, and Timetwister.
I've owned three of the five Moxen (Jet, Pearl, Ruby) and Time Walk in my day (all Unlimited white border), but sold them for well over $100 each. A few other Unlimited white border cards can draw some cash (Forcefield, Gauntlet of Might, Berserk, Chaos Orb, Illusionary Mask) but most of those are strictly for collector value as they're not major Vintage tourney cards. The rest of the Unlimited "money" cards (the dual lands) were reprinted in Revised as well (and for the last time). Those are well worth having, but the dropoff in potential value from Unlimited to Revised sets is quite severe.
Of course, both Alpha (the first printing) and Beta are both more valuable than their later printings due to the black borders. It might seem weird that a Beta Black Lotus will likely bring more dollars in the market than an Alpha Black Lotus, but the Alpha set isn't actually tournament-legal because they have slightly different card "corners"; leaving them as "marked" cards if included in a tourney deck. So if a player wants a black-bordered "Power Nine" card, they have only the Beta set from which to select.
Lots of nuances on the value scene for older cards and value is pretty consistently driven by either rarity or what's playable at the time.