We want to implement a Remote Event Receiver on SharePoint Online List. But we don't want to use Provider-Hosted Addins. Is there any way to have a event-based application which listens to a SPonlie list (remote event receiver) without using a SharePoint Provider-hosted Addin? e.g. by using Azure App Service?
Remote Event Receiver works only as a Provider-Hosted Add-in. You can host your *.svc files whenewer you want on-prem/Cloud.
SharePoint Webhooks are in preview right now but it's closer to your requirements https://dev.office.com/blogs/introducing-sharepoint-webhooks
Another alternative if you don't want to use provider hosted add-ins is to build the application/RER in PowerShell or as a compiled CSOM application. You can then run these on schedule from either an on premises server or from an Azure server in the same region as your tenant (for best performance).
Typically, your provider hosted add in is the UI layer and is going to be communicating to your App Service. I haven't seen any App Service only things communicating to SPO directly, but that doesn't mean there might not be other people doing it.
Technically speaking, you do NOT need a provider hosted app to run a remote event receiver. You only need a WCF web service hosted somewhere. The Visual Studio tooling for Remote Event Receivers does require a Provider Hosted App project template, but you could just write a WCF web service and hook up the dependencies yourself.
You will need the AppForSharePointOnlineWebToolkit Nuget package, which provides the interface IRemoteEventService that your WCF service will inherit from. Then you'll need to implement the ProcessEvent and ProcessOneWayEvent yourself.
If you are calling back into SharePoint from your RER, you will need a way to authenticate however, and an app does help with this. The alternative is to use stored credentials and call into SharePoint using SharePointOnlineCredentials.
If you do need to call back into SharePoint from your RER, have you given any thought about how you will authenticate?