Where can I see my highest spree?
The only stat tracking that is available currently, is what is shown in your profile.
You can access someone else's (Or your own) profile by right clicking on their name or portrait and clicking "View Profile" - At the window appearing in the top left corner, is the stats mentioned.
The stats shown track
- Achievement Points
- Total Elite Kills
- Total Gold Gathered
- Highest Hardcore Level
- Lifetime Kills
(Note that these stats are not specific for each character, but rather account-wide, spanning all your Hero Characters on the specific server you are currently on.)