Of course there can be no "worst" algorithm, since for any
algorithm taking $p(n)$ steps on input of size $n$, we can
easily design another algorithm taking $2^{p(n)}$ steps,
which will be worse by the big-$O$ and big-$\Theta$
measures.

Meanwhile, the phenomenon of extremely long-running
computations is naturally related to the phenomenon of
fast-growing functions, such as the Ackermann diagonal
function,
whose values---and hence whose running times---are
extremely large in comparison with conventional algorithms.

For example, here is an algorithm that is likely to be
worse than any algorithm you may have considered. The
problem is to determine, on input $n$, the $A(n)$-th digit
of the decimal expansion of $\pi$, where $A(n)$ is the
Ackermann diagonal function. On input $n$, my proposed
algorithm would first compute $A(n)$, and then compute
$\pi$ to that many digits, and then output the
corresponding digit. The running time of this algorithm
will exceed the Ackermann diagonal function, but it is not
clear how one could improve the algorithm to make it
faster.

But perhaps you meant to inquire merely about feasible
algorithms, that is, algorithms that we will actually want
to undertake. In this case, of course, even the exponential
algorithms that seem to be required for NP problems would
be too hard, and we would want to stay within the
polynomial hierarchy. Even $n^3$ algorithms are not really
feasible on large input.

(But indeed, I go further, if you are truly interested only
in actually feasible, practical algorithms, then the
big-$O$ and big-$\Theta$ concepts are not the right
concept, since even constant time $O(1)$ algorithms can be
unfeasible, if the constant is very large. The whole point
of big-$O$ and big-$\Theta$ is to look at asymptotic
behavior of the algorithms on extremely large input, and
this takes us immediately out of the actually feasible
category.)