Gmail is certainly the most well-known and seems to be well-liked. However, some people object to the way that it automatically scans all your mail, in order to append relevant advertising material:
http://www.privacyrights.org/ar/GmailLetter.ht m
GMX Mail is the 'new kid on the block', as far as its English language service is concerned. (It only started in November last year). However, it's based upon their German-language service, which has been around since 1997 and generally seems to get good reviews.
My own preference is for Gawab (which is based in Egypt). It's an excellent free and reliable service, which offers both web-based and POP3 mail, free of advertising. Start by setting up an account, here:
http://www.gawab.com
Click 'More Countries & Cities'. I usually select 'gawab.com' as the domain name. Fill in the relevant fields. When you get to the bit that asks if you object to certain types of advertising, simply select the lot (and then you'll get no ads).
Once you've set up an account with Gawab, you'll be able to access it from the web. To access it with Thunderbird, set up a new account with pop.gawab.com and smtp.gawab.com as the POP3 and SMTP server names. Your username should be your
full e-mail address and you need to ensure that 'Outgoing mail authentication' is enabled.
Chris