Currently I track how much money I owe people by emailing myself. Is there a web application for simplifying this with decent email support - ie. I can email it who I owe, how much and what for and which will let me know if it couldn't understand the email?
Billmonk definitely. It sends emails whenever a new bill is shared among users, you can shuffle debts when many people owe money to others in the same group. It supports receiving instructions via SMS emails (SMS sent to an email address), but I'm not sure if a regular email would work though.
Update: Billmonk regularly fails to work correctly (repeating bills haven't worked for months now) and I wouldn't recommend people to use it anymore until everything is fixed.
What about using something like Evernote and just email it the text you want. It won't parse it for you or store it in special fields... but if use a convention such as "John owes me $5 for lunch", you could easily enter a search term like
intitle:"John owes" to find all those notes. They also give you an @evernote.com email address which allows you to create notes via email.