Help with jailbreaking and Cydia for iPhones, iPads, and iPod touches.

I'm writing an answer here because this kind of question often shows up in Google. Right now there's no way to expand Cydia's limit on the number of packages available from installed sources; see saurik's explanation here about why Cydia has this issue:

[Cydia] downloads all of the package listings locally, and then APT consolidates them into a single efficient data structure that can be used even on memory-constrained devices to access the massive wad of packages later. This data structure is only able to store 65k package name entries. There are fixes for this in recent years, but it will require some work to figure out how to safely deploy them (as APT is sadly designed in a way where you can't just quite swap out the library: you have to swap out the apps using the library at the same time; this is why there is that massive mess of APT 0.6/0.7 packages, from the last time I upgraded to the latest version of this cache format).

To get rid of the red error message and be able to use Cydia again, you just have to remove some sources. See the FAQ's guide to Cydia error messages:

Wow, you exceeded the number of package names this APT is capable of.
Problem with MergeList [file]
The package lists or status file could not be parsed or opened.

You have more than 65,535 packages available from your installed sources, and Cydia cannot handle this many. Go to Manage -> Sources on iPhone and iPod touch (or Sources on iPad), tap "Edit" at top right, and remove some sources. It's recommended to keep the stock repositories (BigBoss, Cydia/Telesphoreo, Dev Team, ModMyi and ZodTTD/MacCiti).

Also, if some sources seem to not have a "remove" button when you try to remove them, that usually means they were installed as packages. Go to Manage -> Packages on iPhone/iPod touch (or to Installed on iPad), find the package with the source's name, and uninstall that package.

Note that the default sources have approximately 41 thousand packages available. This leaves approximately 24 thousand spots for other packages from non-default sources. As long as you stick to using sources that don't contain pirated packages, there is room for a lot.