There are 2 different ways of using the pedal on a keyboard instrument.
- You're unable to do a proper legato between notes and you'll cover it with some pedal.
- You use it because you think it sounds better.
The boundary between these two approach is slight but it exists. Let me give you some examples.
Most '800 romantic music is supposed to be played with a good dose of pedal (see Debussy, Schumann and probably many other which I've not played so I won't touch). If you try to play it without, some passages just sounds awful: they're impossible to be interpreted properly with 10 fingers and no pedal.
On the contrary, Bach music is not supposed to be played with a pedal at all (opinions are conflicting but it is widely accepted that the pedal usage should be really limited when playing cembalo music on the piano). Still, if you adopt this approach you'll have a very hard time trying to cover up some passages (but it is not impossible).
If you play Bach you'll notice that ALL of his music is supposed to be played by 10 fingers but not necessarily a pedal: the only way to correctly interpret this music is with a proper fingering.
Here, look at this snippet of Bach partita in E minor:
It would be very tempting to play that descent of 6th in the second beat with just one hand and cover the staccato with some pedal (or just not cover it at all). This would create a gap between each one of those descending 6th which would sound like a staccato.
How would you cover that? Pedal? That's what an amateur would do. Check the great pianists:
Do you hear any gap? Nope. Do you hear any pedal? I don't. So, how do they do that? Proper fingering. If you notice, the right hand has a very simple theme to play: why not use some free fingers from the right hand to "help" the left hand? The first time I was trying to do that my brain exploded but everything which is possible can be learned. For example it is impossible to play a progression of 6th with one hand without gaps or finger substitution.
There are thousands of these little "problems" in Bach music and all of them may be overcome only with proper fingering (and by leaving the pedal).
Now, let's move on to another repertory. Here, listen this classic: Debussy, Claire de Lune. Could you even try to imagine this piece without a pedal? If yes, you're either mad or deaf.
If you want even a more extreme example of something which cannot be played without a pedal, why not listen a piano transcription of one hugest and most magnificent orchestration of all times? Wagner for piano. You can't possibly play that without a pedal: I'm still wondering how you can play that with just 2 hands, let alone without a pedal...
Straight back to question, I hope you'll understand that is impossible to answer it without a reference to a particular passage/piece of music. However, since you're concerned about using the pedal too much a very general piece of advice which helped me is: when approaching a new piece of music, keep the foot away from the pedal. Totally.
Try to let it sound good without the pedal: if you need to blend the notes in a well-sounding legato just try a more wise fingering.
When you'll find a gap or an aesthetically unpleasant passage, you'll eventualy be ready to use the pedal to cover it up but please... Make sure you've studied without the pedal before.