Most of the VF pages in my company org use remote actions, so in debug log the operation is coming as VFRemoting. I need to open many log files to find out the Apex class that has the remote action method I am interested in. For ex, If I need to view the Sytem.debug value recorded using a remote action in controller A, I need to open a few log files and apply filter for Controller A. Is there a way available to search for a word in all the log files shown to me in the log section?
It isn't currently possible (Summer '17) to use the native tooling to perform a search over the contents of all the log files.
You can do SOSL searches over the body of Apex classes and Triggers, but that isn't going to find you content in a Debug Log.
Searching over the Debug log content would require pulling the bytes of each log down and then searching them locally.
Update: I'd seen some posts recently about using the SFDX command line and GREP over the last N logs. It will still need to pull down the entire log(s).
sfdx force:apex:log:tail --color | grep USER_DEBUG
I'm a part of a team that has been working on Maven Tools for Salesforce, a Google Chrome extension that offers you a collection of Salesforce developer tools and it can help you with this issue.
With Maven Tools you can open, search, delete and export multiple apex debug logs at once. As you can see in the image below, you can select up to 200 logs in the list and then search the text you want. The logs where the term was found will be marked with an 'eye' icon. Also, when you open the log it will immediately scroll to the line where the search term was found.