Strings do a lot to the sound. The lighter the strings, the brighter the sound. Usually 12's are considered a "Light" guage for acoustic. I personally play a lot of fingerstyle and prefer Martin Extra Light's (10's) because of their brighter tone and their ease of play. Keep your strings clean (wipe them down with a cloth after use) and if you notice your guitar sounds flat or muted, change your strings.
A very big factor is the wood. Different woods have different tones. This is why we call them "Tonewoods". Mahogany is very deep and warm, cedar is relatively deep. Spruce and Rosewood (One of the most popular combinations) are both mid-range with a pretty well rounded tone. Maple has a tendency to be very bright. One of the popular woods for inexpensive guitars is Whitewood. It's tone is lacking in most cases and the sound does not carry or ring out well.
The nut and saddle you use can have an impact. Bone nuts and saddles reverberate better than plastic, giving you a clearer, longer-sustaining tone.
The way the internal bracing is designed has a very large impact on tone. Brace positioning decides the resonance. In other words, if you don't have good bracing, the guitar may sound muted, lack bass, and have weak tone.
Action helps. If your action is off you may find fret buzz. It will also be harder to play if the action is set too high. This can cause you to have more problems holding down your chords which makes the song sound worse.
The string pegs can influence. Again, plastic does not reverberate well. A set of wood or brass pegs is a small investment that can make a big difference.
Overall construction IS a factor. Solid construction with tight joints causes sound to reverberate better.
Dovetail neck joints generally provide better tone than bolt-on necks.
The number of pieces of wood used can have an impact, because if sound waves have to travel from one piece of wood to another, they lose potency in the process.
Also consider that price is not always a sign of quality. I have a Morgan Monroe which goes for about $450, and all my martin and taylor players fall in love with it's tone and playability.