My suggestion would be Google Mail or Gmail. I have been with gmail for a long time and I have seen it grow to tremendous heights. Gmail has grown into a perfect web based client, become as good as outlook and in some cases even surpassing in functionality.
Earlier I have been a user of Hotmail which used to have an inbox limit of 10mb! I am sure that is not the case now, thanks to all the competition by Gmail on offering gigabytes of capacity for your inbox.
I have also used Yahoo Mail which terminated my account a couple of times when I failed to login once every month or whatever duration they had decided back then. I am sure that has changed as well.
But the whole point is that can you reply on services which come from such a background.
Gmail was the first service which allowed you to integrate your pop mail accounts and import emails from existing accounts with other service providers. You are also able to map your other email accounts and while composing emails send emails from that account.
There have been many doubts about so many people depending on Google for so many things. What if it goes paid all just for suddenly? What if Google sells our data to someone?
Well I feel that Google is in high capacity of delivering the same standards in an ongoing manner which I have failed to see in other service providers.
However, in my recent travels I came across many travelers and surprisingly none of them had a gmail account and hotmail seemed a more popular choice with Britishers.