Mileage Credit Cards - Clarification

Clarification - what I am looking for is the following -
Visa or MC credit cards or other - not necessarily afilitated with an
airline that store/accummulate miles that do not expire, that are
available
for transfer to any airline mileage program (I have Lufthansa and
United because of where I live and where I travel) when I need them -
and not afiliated with BOA (BOA helps illegals). Sometimes I use
United
(Mileage Plus) and sometimes Lufthansa (Miles and More) - but these
miles
are "trapped" in one program or the other and are sometimes subject
to
expiration dates. I recall hearing that these credit cards exist,
just can't
recall which ones. Thanks in advance for any ideas.