i'm not sure server should be doing that - frontend might be a better choice because it could prompt user and show the information to user before submitting. additionally, we should support multiple methods of submitting the information, because zabbix installation might not have direct access to internet - sending an email (requires configuring smpt params), posting to webpage (would require http proxy support) etc.

anyway, initial list of things we might be interested in (initial list should be as inclusive as possible) :

unique id (how to construct one ?) so that changes in data might be seen afterwards;
zabbix installation age (how is it determined ?);
db used;
db size, if possible
zabbix version;
upgrade history (would require updating db schema like adding some fields like version, date, added when new version is run);
host count; monitored directly/through a proxy
template count
max templates linked to single host, avg templates linked to single host
max template linkage depth, avg template linkage depth
itemcount
triggercount
max items referred to by trigger, avg items referred to by a trigger
action count
action count using escalations
action count using recovery messages
custom graph count; max items per graph, avg items per graph
proxy count, max/avg hosts per proxy
event count, events per day
notification count per day
usercount (disabled, with api access, with gui access, last log in times - to know how many are actively used)
usergroupcount, users per group
maybe some usage statistics - auditlog table actually already has it all, it just has to be extracted in a meaningful way - like how often an item is modified, how often a new host is added etc
average login frequency for users
frontend language used (users per language)
frontend theme used (users per theme)
network map count
custom background images uploaded
custom icons uploaded
max element count per map
avg element count per map

this post should be edited to add more/improve existing

here's what opennms does : http://stats.opennms.org/

For security freaks the process of gathering data can be organized as follows. Server will dump usage statistics into its database where it may stay undisclosed forever if the user is not willing to help improving Zabbix. But for those who are Zabbix will provide a standalone utility to extract this data from the database and generate a human-readable report in plain text file or XML. This file can be then reviewed for the presence/absence of any sensitive information and submitted manually in a special user feedback corner of https://www.zabbix.com.