Most of the time we can live without them.

There are 2 ways of connecting to services on the internet.
The first way uses the client-server model.
A client opens a connection to a server, and gets access to the services offered by the server. Since you are always the client (you don't run a server), you always open an outgoing connection, and you don't need incoming ports.

The second way uses the peer-to-peer model.
Basically you are sometimes a client, and sometimes a server. Which one you are is determined for every connection. You can be a server for one connection and a client for another at the same time.
To act like a server, you need the incoming ports.
If you don't open the incoming ports, your p2p application can only act as a client, not as a server. Therefor, it cannot make as much connections, and it may be slower.

So unless you run a server at home, or you use p2p, you don't need incoming ports.

note: p2p is not only BitTorrent, eMule,... there are other applications too. I once saw a p2p online radio streamer.