The rules of thumb mentioned above are important, but each check is an individual item and has to be judged on its own merits. Some payees might be more desirable than others - for example, this Ralph Kiner check written to "Kiners Korner Inc" (and bearing a printed Shea Stadium return address)...
...and endorsed as such on the back, in his own hand...
...might have greater appeal to someone who has fond memories of the "Kiner's Korner" post-game show following Mets broadcasts more than a similar Kiner check made out to The May Company or White's Drug Store.
Sometimes, it's what the check was written
for that makes a check important. For example, this Casey Stengel check made out to "Essex House"...
...with "NY Expenses NY Mets" written in the corner. What makes this check particularly significant is that it was written October 12, 1961, two days after the expansion draft in which the players who would comprise the inaugural 1962 Mets were selected. Unfortunately, the bank cancellation holes go through the words "NY Mets," but that doesn't take away from the historical value of this particular check.