If you mean that only the data tables are in Access and some other program provides the user interface, then yes. If the user interface is part of the mdb, then no; either the full or runtime version of Access must be installed.
You'll find that a lot of people do this with Visual Basic apps. You can connect a simple VB app to an Access MDB file just to get it's tables. In fact, using DAO (Data Access Objects) you can have your VB app *create* the MDB file on the fly.
Now - if you're asking whether or not you can distribute your Access database to people who don't have Access, then YES you can, but you'll need either the Access Runtime version (which you can give away royalty free) or you'll need the Access Developer Extensions (you have to pay for these with Access up to 2003, free with 2007).
Yes, you can use an Access MDB in your application. There is a well-known way for old VB developers using DAO. You can use the same method in .NET by creating an interop reference. The other way is to use ADOX library.