I don't know Microsoft's upgrade policies, but yes, you can convert an
Access95 database to run under 2007. I won't say "without problems" because
the user interface in 2007 is quite different (the "ribbon" is new, custom
toolbars are either gone completely or much more difficult), but a
plain-vanilla database should upgrade OK. There is also a lot more rigorous
security in 2007 but there are web resources available to explain those
problems.