To delete your Angie's List account, you apparently have to contact them by phone: 1-888-944-LIST (5478).
However, one of our users pointed out that they aren't to keen in helping you out unless you really push things hard. Not good.
Because an account at Angies List cannot be deleted, we suggest to make your data useless.
Be logged in on the site, then go to Profile Settings (Or Options, etc.). In all fields with personal data (such as name, address, city), fill in AccountKiller, if possible. If you can only choose from several options, change the value. If possible, use a homepage/URL field or long text field (such as Description) and put this line in it: https://www.accountkiller.com/removal-requested. This may incite webmasters to add an account deletion option.
Publicly visible text/images often aren't properly deleted even when you succeed in deleting an account. Try editing or deleting them manually before deleting the account itself. If you're unsure what happens to your tracks: this can be found mostly in the Terms of Service/Privacy Policy; otherwise you can always contact Angies List and ask personally. By the way, deletion requests don't necessarily mean your data will actually be deleted (e.g. due to legal obligations).
If you can't find any contact info and still wish to ask something, for example a question about what exactly is deleted, about data retention, etc., you may contact the domain owners using this info.
If you signed up for Angies List using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Angies List. Click the icon below to find out how.