In Guitar Hero, what visual (e.g. the flame), audio, and on-screen score feedback did you immediately get when you hit a note accurately? And what visual, audio (the bad note sound?), and on-screen score feedback did you immediately get when you miss a note by playing it early/late, or by not playing it at all?
This video clip demonstrates what happens when a note is missed.
There is a small twang sound along with the song volume going down for a second. Along with those audio ques, the "note highway" will shake and you will lose your combo multiplier.
I'll start by noting that the feedback is mostly consistent across all of the Guitar Hero games and Rock Band as well. There's a few differences between some of the later Guitar Hero games, though, thanks to some mechanics added in. In any case, I'm not going to cover the stuff added by GH:WoR.
Visual feedback (on the note highway)
When you hit a note, the gem(s) for that note will either erupt in flame (Guitar Hero) or burst (Rock Band). In the case of sustains (long notes), the note tail will light up. Hitting all of the notes in a "Star Power" or "Overdrive" phrase correctly also produces its own feedback, which is either lightning bolts (Star Power in Guitar Hero) or a yellow pulse from the note highway (Overdrive in Rock Band). In Rock Band 3 in particular, when you have a 4x (6x on Bass) multiplier without Overdrive active, the note highway will have a blue background on it (which goes away if you lose that multiplier due to a combo break).
When you miss a note, that gem will not erupt in flame or burst, and in the case of sustains, the tail will darken and become grey. If the missed note was in a "Star Power" or "Overdrive" phrase (indicated by the gems being stars [Guitar Hero] or white [Rock Band]), the remaining gems in that phrase will revert back to their normal appearance.
This is pretty much straightforward. There's a combo indicator (typically right next to the multiplier and, in later games, situated alongside the note highway). hitting successive notes correctly will build it up (until you have a maximum multiplier - 4x in most cases), making an error will cause it to reset.
I am assuming you haven't touched any of the mixer settings, since some of them do affect audio feedback. Whenever you break combo (for any reason at all), the instrument channel for your part is immediately lowered in volume (to a certain minimum, which is different depending on the game). In the case of drums, missing a note entirely will only lower one part of the drum mix, while erroneously playing a note that isn't there will lower the entire drum mix's volume (if my memory serves me correctly). Playing correctly will bring that part's volume back up to normal. Playing notes where there are no notes (excluding certain sections on drums) will also produce a "miss sound" (which, in some games, can be disabled).
In the case of drums, both Guitar Hero (starting from Guitar Hero: World Tour) and Rock Band have "Drum Fills", although they're done differently in the two series of games. In the case of Guitar Hero, it's large sections of no notes being present where the drummer is allowed to play whatever he feels like without penalty (and in Guitar Hero: World Tour, they would actually gain one point for every note he played in a drum fill). In Rock Band, however, fills only appear for the drummer if they have at least half of their overdrive gauge filled, and at least 4 notes must be played during the fill (3 notes on any combination of surfaces and then a green note [red if lefty-flipped] at the end) to trigger Overdrive. There is no penalty for missing a drum fill in either case, but in Rock Band, the drum stem from the song is completely muted during a drum fill and is brought back up in volume on the next non-fill note.
I can add that, if you have calibrated lag, any feedback from above will be delayed by the amount of video or audio (depending on type) lag that is there (and that you have probably set.) So if you have a TV with a lot of lag, it can be a bit scary not to see the "flames" immediately after hitting the notes, even if it sounds in sync to you. I would say, with a lot of lag, trust your audio lag setting and what you hear over all else.
Other answers have pretty much described the feedback itself.