  In the proof of the irrationality of $\zeta(3)$ and $\zeta(2)$, Ap\'ery
defined two integer sequences through $3$-term recurrences, which are known as
the famous Ap\'ery numbers. Zagier, Almkvist--Zudilin and Cooper successively
introduced the other $13$ sporadic sequences through variants of Ap\'ery's
$3$-term recurrences. All of the $15$ sporadic sequences are called
Ap\'ery-like sequences. Motivated by Gessel's congruences mod $24$ for the
Ap\'ery numbers, we investigate the congruences in the form $u_n\equiv \alpha^n
\pmod{N_{\alpha}}~(\alpha\in \mathbb{Z},N_{\alpha}\in \mathbb{N}^{+})$ for all
of the $15$ Ap\'ery-like sequences $\{u_n\}_{n\ge 0}$. Let $N_{\alpha}$ be the
largest positive integer such that $u_n\equiv \alpha^n \pmod{N_{\alpha}}$ for
all non-negative integers $n$. We determine the values of
$\max\{N_{\alpha}|\alpha \in \mathbb{Z}\}$ for all of the $15$ Ap\'ery-like
sequences $\{u_n\}_{n\ge 0}$.The binomial transforms of Ap\'ery-like sequences
provide us a unified approach to this type of congruences for Ap\'ery-like
sequences.
