When a accelerando and ritardando is not written, is it bad to speed up and slow down where you think it “sounds better?” This seems like against practicing with a steady beat, because it makes a metronome useless.
I think it depends very much on the genre, style, and period of the music.
For some styles, heavy use of rubato is normal and suits the way the music is written, while for others it would spoil the piece. (Think how bad a rock song would sound if the drummer kept varying the tempo!) Even within Western classical music, rubato is much more common (and expected) in, say, Romantic pieces than in earlier Baroque. There are always exceptions, of course, but you must be sensitive to the composer's intentions.
For example, there's a recording of Bach's French suites that I find unlistenable due to the inappropriately-high levels of rubato employed. The performance style would probably work well for, say, Beethoven, but to me it just sounds terribly out-of-place and vulgar for Bach.
There have been times over the last couple of centuries when people seemed to think that every piece of music should be played the same way! Thankfully, historically-informed performance has become more popular, and people are at least aware of alternatives.
So it partly comes down to understanding the style of the piece, understanding what the composer intended and how people of the time expected it to be played.
However, it's also down to your judgement and personal taste! Ultimately, if you're performing the piece, you have the final say, and shouldn't be playing anything you're really not happy with.
Finally, you should certainly be able to play a piece well at a steady pace, without any rubato at all, adding expression in other ways. Then you can judge how much (if any) is justified.
It's not bad per se, but it's dangerous.
Making this a habit will impair your ability to play with others.
As an expressive device, varying the tempo can be distracting. (That's why it's notated more rarely than varying the dynamics.) The exception that proves the rule here is instruments that can't vary dynamics. When one famous harpsichordist "held on to a fermata, worlds tottered and the sun stopped until she went on to the next phrase."
Depends. Some people use 'expressive rubato' as an excuse for bad time-keeping. In particular an excuse for playing the tricky bits slower than the easy bits! Flexible time is probably a bad idea in a rhythmic groove-based song. It's almost required in an operatic aria though.
The fact that sometimes a metronome isn't appropriate doesn't make metronomes useless!
As Lawrence said, you are describing "Rubato". My professor in college recommended playing the piece first at a more "rigid" tempo and then using your own discretion. You want rubato to feel tasteful enough so that a professional listening in the audience could dictate the rhythm you played without seeing it.
In general, a solo will have more rubato and adding more instruments will tend to make the tempo more rigid. That being said, conductors with good vision and execution can train a group to perform rubato together.
Some metric flexibility in certain pieces can make them heartstoppingly effective. The best way for you to convince yourself of this is to listen to some recordings. I will suggest two:
Brahms Sonata for Cello and Piano in E minor, 2nd Movement. Contrast the Rostropovich & Serkin recording, which has quite has a quite subtle give and take with the meter, and the Maisky & Gililov recording, which shows greater flexibility. Both are perfectly valid interpretations. Listen to the whole movement of each.
A prelude of a Bach cello suite. I will let you listen to several different interpretations yourself to identify one with more flexibility and one with less.
This is an actually precarious question since wanting to hear a particular answer makes it likely that you are in danger of overusing that answer. Timing is a very strong part of how music is interpreted. To actually work in that manner, every change must be recognizable as deliberate without acting as a distraction or mask. So the way to employ timing variations as an expressive ability is a very, very good control over the precision of timing. This is complicated by your sense of timing getting distracted by actual playing, something that the listeners are not exposed to.
So it usually requires a lot of metronome (or drum computer) work and recording and listening and discipline and good control of the piece (basically, you should be able to play everything 20% faster than at performance speed without falling apart) to effectively employ timing as an expressive device in a tasteful while unambiguous manner.
Changing tempi is part of good performance practice, in my opinion. As noted above, we do it less in earlier than in more recent music. But I can't imagine that a player or singer in Bach's day would have resisted imparting a bit of give and take on notes he or she found particularly engaging. No one disputes a certain "allowable" range of base tempi for a piece, even for early music, and discreet rubato here and there is not that different. Where I do have a major problem with rubato is if one or more notes are held so long that the listener might sense metric change where there is none, as, say, if 3 triplet eighth notes were played or sung such that the last of the three was extended to twice its written length, making the whole sound more like a 2 eighths and a quarter.