The ones I am aware of for delay differential equations are:
For other types of ODE’s the page of Hairer includes several codes for both stiff and non-stiff problems. I believe many of them are heavily used across various fields.
Another classic resource are the ODE solvers published at netlib. Unfortunately, most of them are F77 style codes which are not thread-safe. An exception is the rksuite which has a Fortran 90 interface and was later modified and included into the NAG library.
The blog post from Christopher Rackauckas (also listed above by @kargl) lists a few more Fortran codes including ODEPACK, Sundials, and FATODE. Many of these are still heavily used today. Some of the solvers by Hairer and from ODEPACK are wrapped in scipy.integrate.
Concerning performance and design, as Christopher states:
DifferentialEquations.jl does offer pretty much everything from the other suite combined, but that’s no accident: our software organization came last and we used these suites as a guiding hand for how to design ours.
As far as stiff problems are concerned, many of the older Fortran packages don’t use LAPACK for the matrix factorizations but their own factorization routines. I believe with some small refactoring performance could be improved. Still it would take a prodigious effort to reach the same level of comprehensiveness that has gone into DifferentialEquations.jl. The author of that package lives and breathes differential equation solvers.