Other answers have touched on the need to make sure the computer uses a standard architecture.
The problem with buying a new motherboard for an old computer is that you'll pretty much have to buy new RAM and a new CPU to go with it. THrow in a new hard drive if you can't find a board that supports IDE, and you're very quickly looking at close to $200 or more.
If you are looking for an inexpensive way to replace a dead motherboard, buying a used motherboard on Ebay may be the way to go.
You can easily find used but fully functional obsolete boards there for around half the cost of a new motherboard, and if you are comfortable and familiar with assembling computers from parts, finding a used good-quality motherboard that is compatible with the dead computer's RAM and CPU will give you a working system for much less than the cost of a new motherboard + new CPU + new RAM, etc.
Just be careful to only buy from sellers who guarantee the board will work, and stick with a brand name board (Intel, Gigabyte, etc).