Arduino Newbie: Solderless Breadboard Alternate
Breadboards are for development and testing. When you are OK with your circuit, then you solder it.

Your alternatives:

Point-to-Point

Just solder directly component to component. You can arrange your component for minimal space and minimal wiring length. Can be very elegant (depends on your abilities) and doesn't require any board. 



Perforated board

For personal projects, you can use a perforated board to put all your components. Requires some planning in components placement and wiring (you can paint yourself in a corner). Easy to do.



Expansion Shield

It's a perforated board on a shield, so you just plug it over your Arduino Uno. Great if you need easy access to lots of Arduino pins. Cons: little space for components. There are versions with a mini-breadboard instead of a perforated board.



PCB

You can make your how PCB, but it's hard and too much work. Use it only for high volume production. It require lots of preparation and dangerous chemicals.



Useful links (YouTube)


Review of some prototype circuit building methods
Perfboard Prototyping
Breadboards &amp; Perfboards