Basically a member of any tribe could marry any other tribe; tribal identity is passed through the father. If Susan, an Asher-ite, marries Bob, a Levite, their children are Levites. (You'd probably still identify Susan herself as being from the tribe of Asher, but it doesn't affect that much. E.g. we're told that Samson's father was from Dan, but his mother from Judah.)
This is still relevant today as some Jews have special status as Levites, and a subset of them are Kohens. Some think it's more prestigious for a kohen to marry a woman from a kohen family, but this is clearly not required. (The Talmud says the kohen gadol -- high priest -- could just as easily have a non-kohen mother.) Marriages between Levites and non-Levites happen all the time. (The average non-Levite today is most likely descended from Judah, given the population numbers, but it's kind of moot.)
The portions of ancestral lands were parceled out in big chunks to each tribe. That means you'd have, eh, let's call it 1000 acres, each acre belonging to one member of the tribe Zebulon. If Joe Zebulon dies and leaves only a daughter, she inherits that acre; if that daughter marries Bob the Reubenite, then their (Reubenite) children will inherit that acre. That means you could have one "Reubenite" property in the middle of a giant block of Zebulonite properties. Not a big deal.
The last chapter of the book of Numbers actually addresses this situation; the first generation entering Israel had a tricky legal status as they were trying to map to the population one generation prior (i.e. those who exited Egypt); therefore female heiresses then had to marry within their tribe. The Talmud makes it clear that this was a temporary restriction on that generation -- once the land was parceled out, it could change hands.
See the link for more -- the Talmud discusses it in Bava Bathra 120a.