Hi-fi is pretty subjective - some people are happy with a €100 hi-fi that sits on the kitchen worktop, some will spend literally 1,000's to get the best from a system, including spending what seems like riduculous money on components such as inetrconnects, speaker cable, etc. The choice and cost is endless. Horses for courses.
It is undeniable there is a huge difference between an entry level hi-fi and a 'boom box' that flashes and warbles. I had a pretty basic / bottom line marantz CD player for over 10 years, friends agreed it sounded amazing when the heard it. When it eventually died (laser packed in, not worth replacing), I traded up to a Rotel - it cost about €600, a good mid-range player. It certainly sounds more convincing over the marantz - instruments are more realistic, well placed in the sound stage and it handles complex pieces of music well due to its higher sampling rate (24-bit/96kHz). All in all I'm very happy with it.
I agree with Aldark in that the quality of the system has to be matched - my CD player paired with a crappy amp will not do it any justice. Spend the money wisely and you'll have a system that puts a smile on your face whenever you spin a disc.
Looking back, here are a few pointers I would add when choosing a set up:
1. Most important is to listen to a set-up and hear what is good for you. Some people prefer a warmer sound (an Arcam will gernally deliver this), to a more pure / atatcking sound (Rotel, maybe NAD, will generally deliver this).
2. Power rating - don't get hung up on Watt rating of amps. My Rotel amp is 40w per channel - this is plenty to fill an average medium sized living room. Don't let a salesman flog you a leviathan that will over power your space. Upgrade options worth looking for in an amp include pre-out (for pairing it with a power amp), 12v triggers (for remote operation, for example a wall mounted key pad in another room), a remote control, plenty of inputs (for CD, radio, turntable, casette player, DVD etc etc), switched paired speakers (i.e. that will run 2 pairs of speakers - handy for separate rooms)
3. Bear in mind that that lower impedance of a speaker will challenge an amp - the lower the ohm rating, the harder it is for the amp to work the speakers. Most speakers are in the range 4 - 8ohms (floor standing speakers tend to have a lower impedance). This may also have an impact if you run 4 speakers from an amp - a good amp will generally olny handle a max of 4 ohm when both speakers are running.
4. Spend money on good quality cables, but don't get carried away. 10% of the cost of the system is a general rule of thumb. A good system will be crippled by poor quality cables (for example, bell wire or standard electricalcopper cable). It's all about conducivity - the more you can transmit down a given cable, the better the sound.
5. Get your hands on what hi-fi / hi-fi choise magazine and get familiar with what's out there. Not all systems on paper will sound the same.