This seems to be a fairly common request on the Salesforce forums that developers frequent.
REQUEST_LIMIT_EXCEEDED: TotalRequests Limit exceeded.error about?
How can I found out what caused me to hit it?
How to determine what is making the API calls?
How can I get insight into an API call that took place on a certain date for one of our connected apps?
First, some context. This is the Total API Request Limits limit. It is a rolling limit for an organization over the last 24-hours. This means an API call made just now will count towards that limit until 24 hours from now. Don't expect the limit to reset back to zero at midnight.
The exact size of this limit depends on the Salesforce Edition and the number of per user licenses of a given type you have. It is possible to purchase additional API calls without needing more user licenses.
There are two locations where it is easy to check the current API usage.
Under Setup > Company Profile > Company Information there is an API Requests field. This will show you the current API call count the the maximum you can reach.
Then, within Reports > Administrative Reports there is API Usage Last 7 Days
This provides slightly finer detail, such and the username that held the session and the Client Id that was used to make the call. The Client Id can be useful as it can identify which external app was consuming the API calls.
Receiving a warning
You can configure an email alert to a user when the API requests exceed a percentage or you maximum requests. This is a RateLimitingNotification record that you create from Setup > Administration Setup > Monitoring > API Usage Notifications.
Monitoring via the API
The SOAP APIs have a LimitInfoHeader that can be used to monitor API usage.
Event Monitoring API
The Event Monitoring API can provide much finer details about API calls over a wider history. With this (paid feature) you can see exactly what API calls were made in a time period.
E.g. From the developer console query editor
select Id, EventType, LogDate, LogFileLength from EventLogFile where EventType = 'API' and LogDate = 2016-02-20T00:00:00.000Z
Look for the EventType of API and the LogDate for the UTC day of interest. Unfortunately there isn't a single comprehensive EventType that will allow you to monitor all events that contribute to the limit. There is also the Bulk API, Metadata API Operation, and REST API.
You can then pull down the single `LogFile` data, which is a base 64 encoded CSV with all the API calls for that day.
select Id, LogFile from EventLogFile where ID = '0AT700000005WDaGAM'
The FuseIT SFDC Explorer has an Event Log tab that uses the same API calls and will extract the file for you and export it to a CSV.
For the LogFile, look for the USER_ID, CLIENT_IP, and CLIENT_NAME to help identify which app is making the calls.