Replacing the bike seat on my mid-1990s Trek mountain bike
tl;dr: Yes, you can pretty much buy any seat except some rare/expensive racing or classic leather seats.

Explanation: As long as your seat attaches by two parallel rails that are 44mm apart (which is 95% of seats), then you can replace it with another seat that also attaches by the rails. In case you don't do metric, 44mm is just under 1.75 inches measured between the center of the rails.  Here's a photo of a seat with standard rails from wikimedia commons: 



For example, even bizarre noseless seats use the two parallel rail design, visible here (for the record, these noseless designs make it hard to control your bike, so they aren't advisable, also see comment by Criggie):



If you're keeping the same seatpost, then you would normally keep the old seatpost adapter as that's what changes between different bike models (seatposts vary in diameter and some seatposts are tapered at the top). A slight complication is that some rails are 7mm in diameter, some are 8mm in diameter and so forth. Usually the clamps are flexible enough to accommodate that variation. I think your bike is bog standard so you shouldn't encounter any problem. 

The 5% of seats that don't use the 44mm rails include some keirin racing bikes (that use 30mm rails), classic leather seats (like older Brooks) that use four rails, banana seats, children's bike seats, and a few others.