carrieg, I use Excel. Yes, you should keep records, for these reasons:
-- Unemployment requires that you be looking for work. If at any point they question whether you've been doing your part, you need to be able to have the facts ready.
-- It helps you keep all those job descriptions and companies and recruiters straight. Get confused by thinking one recruiter was for the wrong job, and it could lose you credibility, not to mention the job or potential future jobs.
-- It helps you follow up. You can go down your list and see who hasn't gotten back to you and call them.
What to put:
I based by spreadsheet columns on the requirements of PA state's unemployment. The columns:
Date
Company Applied To (if the job is through an agency, I put the agency first, then a slash, then the employer company. You may prefer separate columns for this instead.)
Contact Name & Title
Address
Phone
Email
Website
Job Title
Method of Contact (this was for the unemployment requirement. I don't find it all that useful.)
Results
Other
For Results, it could be anything from a confirmatory email for a web application to a callback, to a scheduled interview, to notification that I didn't get the job. I usually make another row's entry for another contact & just copy the info to the new row.
Other may be notes about the recruiter or manager, any info they pass along, etc.
You may find a different order works best for you or other columns, but this should get you started.
I copy and paste job descriptions into a Word document, which I save in a file for that purpose.