Database in simple recovery to save space
First a quick note on moving to SIMPLE recovery.  This is a business decision.  It is not in any way a technical decision.  Your business needs to weigh the cost of staying in FULL (which may mean a new server with additional space, archiving current data to free up some space, etc) vs the cost of losing up to a day or more of data.  Once they have decided then you can proceed. 

Based on your question and the comments I see one of two scenarios:

You are in FULL recovery mode but are not taking log backups.

At this point you need to start taking log backups on a regular basis.  In all probability this will actually save you space.  If you take a log backup to clear the log less than once a day (Note: FULL backups do not release log space) then your transaction log is probably larger than it needs to be.  Get your backups in order then figure out how big your transaction log actually needs to be.  In all probability it will be quite a bit smaller than it currently is giving you additional space for backups.  Worst case move your backups to tape more frequently than you currently are.

You are in FULL recovery mode but are taking log backups.

If this is the case then you may need to increase the frequency of your log backups.  This will not incur additional space requirements since the log files will just be smaller (there is some small overhead for header info but it's not that significant).  This will allow your log to clear faster and stay smaller.  Assuming (and this is a big assumption) that you don't have one or more individual transactions that are requiring the log space.  If that is the case then only changing your code to decrease the size of your transactions is going to let you get away with a smaller log file.  Even if you switch to SIMPLE recovery you are still going to require log space for the largest single transaction (or largest combination of simultaneous transactions).  If you shrink your log file and run a transaction that needs more space than is avialable it's just going to grow the log again.

Again switching between FULL and SIMPLE recovery is a business decision.  Making that kind of decision without consulting the business (and then being wrong) is a good way to get yourself fired.