[paulpauper]

advantages: no snooping, no deletions , no annoying lockouts if your IP changes, no adds, much less confusing the layout, much better spam filtering, looks more professional, better customer service

disadvantages: monthly or yearly fee, possible downtime issues, more work to set it up

[LinuxBender]

I agree with all of this.

I would add that if you host your own server, then your email is your property. On google, it's their property and they can discontinue their service and purge all content if they so desire. (Not that they would, just saying they could)