I have had 4 online savings accounts. I still have 2 of them currently open. I have INGdirect.com which I haven't had any problems with. I put in $$ automatically every month and never have the urge to touch it.
Also I have an HSBCdirect.com account and I really love that account, little better interest rate, never had problems with the site, etc.
I used to have a EmigrantDirect.com account and the website was always so messed up I was always calling in to get them to reset my password. So I decided if I couldn't get to my $$, then I didn't need to have an account with them anymore, so I closed it.
I used to have a savings account with OneUnited.com - from California run by black entreprenuers. Had a high interest rate 5.25%, but I was always having problems with it too and they only pay interest quarterly instead of monthly....
Good luck in your endeavor!