Certbot and acme.sh are the most popular dedicated linux clients (.e.g. software you would install separately just to manage ACME certificates). The most popular clients on Windows are win-acme, Certify The Web and Posh-ACME.
What's best for you will depend largely on your requirements but for instance a user running linux for fun who wants to use Apache or nginx would probably use either Certbot or acme.sh, but if interested in modern web servers when they'd quite possibly choose Caddy instead. Users who are trying to configure kubernetes would probably use cert-manager.
Organisations which are running custom hosting solutions will either integrate a popular library or just build their own ACME client (some orgs prefer not to have external software dependencies).
There was an old PDF somewhere with more detailed user-agent statistics but I can't find it.
I think those above (and possibly more) are libraries or tools. Sometimes they'll be listed in User-Agent alongside the real client name (dehydrated normally sends its version along with the curl version), but probably some developers are failing to (re)set their User-Agent headers so only the default for the library/tool gets recorded.
Also, the method of generating that table (Table 2) doesn't seem to be given, so it's not clear to me whether, for example, dehydrated is also listed as curl, only as itself, or only as curl.
So those stats may only be telling us which language or tool people are using, not what the clients really are.
Would love to known more current numbers as well. I'm predominantly just an acme.sh client user for integration in my Centmin Mod LEMP stack for nginx default HTTPS - thanks @Neilpang
The top few user-agents, counted by how many different subscriber accounts make new-order requests using that agent, are:
cerbot
plesk
synology
autocert
eggsampler-acme
acme.sh
NDMS
xenolf-acme
BTPanel
The top few user-agents, counted by how many different domain names are in new-order requests from those agents, are:
certbot
cpanel
autocert
Acme::Client (ruby, I believe)
Plesk
dehydrated
acme4j
squarespace
acme.sh
These rankings are very very very very rough. I'm only looking at a few hours of data, I'm not doing anything particularly smart to parse the user-agent, and of course just requests to new-order don't tell the whole story. But I think these are a reasonable proxy, at least.
(And now, because this thread is 9 months old, I'm going to lock it.)