Zeus Trojan steals $1 million from U.K. bank accounts. Harmless? But wait, there's more. This was just a single instance.
The Zeus trojan captures your keystrokes and implements 'form grabbing' (taking the contents of a form before submission and uploading them to the attacker) in an effort to steal sensitive information (passwords, credit cards, social securities, etc.). It has capabilities to infect Windows and several mobile platforms, though a recent variant based on Zeus's leaked source, the Blackhole exploit kit, can infect Macs as well.
Zeus is predominantly a financial-interest malware, however if infected, your machine will be recruited into one of the largest botnets ever. The master could then use your computer (along with any other infected machines of that bot) to be used to do any number of nefarious tasks for him (launching DDOS attacks, sending spam, relays, etc.).
Recent versions of Zeus include crimeware capabilities, P2P spreading (allowing for rapid infections) and secure communications that encrypt data while phoning home for commands and back to the client (SSL). Crimeware allows the attacker to steal, encrypt or otherwise prevent you from viewing or using your important documents and applications until you pay the master.
As if that weren't enough, the Zeus trojan (which previously was sold for a pretty penny on underground forums) source is now available (via a leak), which has introduced almost two thousand variants. The most common of which are GameOver, ABUSE and the Blackhole Exploit Kit.
Harmless, not so much. However, if you're truly interested in understanding Zeus (which is a fascinating and intricate piece of malware) I encourage you to reverse engineering it and analyze it for yourself (in a safe environment of course).