V-Tech cordless telephone with answering machine - model 2650.  This model has been working exceptionally well for us since purchasing it several years ago.  It came with a separate handset that didn't need a telephone jack.

We use it when we are working out in our yard and it works well with the wind and traffic.  We can hear above that noise and the caller on the other end has no trouble understanding us.

The one recommendation is to have a battery back up.  When the power goes out, the answering machine 'clears' and we have to set up the message and time/date again.

We have not had to...