Now that SAP HANA databases are already running for quite some time, I compiled a list from all HANA alerts which happened out there in real life and I stumbled upon. My emphasis is on the distribution over many systems, not the raw number of events because some events can fire quite frequently, albeit on only one database. From many dozens of HANA systems which I saw, containing half a billion 
of alert events, I got this top 3 list of alerts from all systems:
| ALERT_ID | ALERT_NAME | |
|---|---|---|
| 24 |
| |
| 23 |
| |
| 22 |
|
Alert 24 happened the most because it is checked every 60 minutes, alert 23 is only checked every 6 hours and alert 22 is only checked once per day.
OK, I was just joking. Seriously, the table is of course as obvious as it is boring. I don't know why SAP included these meta-alerts, but they are quite annoying and I don't consider them helpful in any way. If you are running a HANA database, then you'll have alerts, it is as simple as that. Now what did I get if I exclude these meta-alerts? Again, almost all databases reported these alerts making them my real top 3 alerts in HANA databases:
| ALERT_ID | ALERT_NAME | |
|---|---|---|
| 58 |
| |
| 0 |
| |
| 3 |
|
My favorite is the alert 58. SAP simply cannot provide a good default size for the HANA plan cache. So every HANA DBA has to initially adapt the plan cache and reevaluate the size in case of alert 58. The optimal size depends on your workload, you don't want to waste memory but you also don't want to impede performance either. The SAP note 1977253 clarifies all questions, for ABAP systems I calculate the recommended plan cache size directly via SQL:
select max(connections)*15*1024*1024 from (select snapshot_id,count(distinct connection_id) connections from _sys_statistics.host_connections group by snapshot_id)
For alert 0 there is no check threshold, I believe this is an error which is raised automatically once the statistics server detects some issues. Also the severity level 5 makes this alert unique. Anyway, here you'll have to dive into the trace files and search for a suitable SAP note to fix this.
The situation for alert 3 is quite similar. "Inactive services" is a very sensitive alert which is probably already known to you. Again, there is no panacea since it is just a symptom for different kind of issues.
For the long tail of all other alerts, the picture is very heterogeneous. Other alerts often affect only a minority of systems or sometimes only certain revisions. Maybe with more time and more HANA databases, I will see some more trends.