Yes, you can track the number of activities completed per user.
Go to Tools > Filters & Groups (Lookup > SQL Queries in GoldMine 7 or earlier), then click on the SQL Query Tab. Paste in this:
select userid, srectype as Type, count(*) as Number from conthist where srectype in ('A', 'C', 'M') and ondate >= '1/1/2000' and ondate <= '6/30/2008' group by userid, srectype
Change the date range to suite your needs. This counts appointments (A), calls (C), and emails (M).
You can send these results to Excel by right-clicking, selecting Output to and then Excel.
(thanks to Chad Smith for this tip)