In VS mode, players may set the difficulty level of CPUs (bots). What're the differences from levels 1 to 9?
Higher difficulty levels make the opponents "better", but they do have an upper limit. I personally found it to be around level 7-8. Level 9 opponents are harder to beat but only because they have inhumanly good timing. For example, they will frequently power shield your projectiles (much higher % chance than most humans, even very good ones), especially in a situation that would be too fast for most players to see coming (e.g. immediately after a missed attack or recovery).
Also they tend to abuse directional influence more at level 9 than you can with a controller as a human, so in some aspects of the physics engine, they are cheating. That may be better or worse for your enjoyment.
If you are a very good player or play with any, practicing against level 9's (alone) won't really help you become highly skilled. SSBM's AI is not particularly good. A human partner at/somewhat above your skill level is best, combined with learning advanced skills (L-canceling, wavedashing, boost canceling, etc).
As I understand it, there are a number of differences between CPU levels, summarized below:
Typically, higher level CPUs have faster "reflexes" - what I mean by this is that even though a level 1 and a level 9 computer are both likely to choose to make the same attack, the difference between deciding to attack, and actually following through with the attack, varies enormously between levels.
For example, though a level 1 CPU and a level 9 CPU will probably both identify using Fox's blaster as the first attack on a flat stage (like Final Destination), the level 1 will usually wait a long time before following through, whereas the level 9 will likely attack immediately (often with inhuman speed).
It is also because of these slow "reflexes" that level 1 CPUs can often be observed standing beside their opponent without actually attacking them, a behaviour uncommon among higher level CPUs. Contrarily, higher level CPUs will use more special attacks, aerial moves, grabs, and tilts, and just generally be more versatile than their lower-level counterparts.
Lower CPU levels are also unlikely to shield or dodge, or as above will do so too slowly, meaning they will be hit by attacks that higher level CPUs would easily dodge. In fact, lower level CPUs will tend to roll out of the way rather than shielding, whereas higher level CPUs will not only shield, but can often Powershield, thereby reflecting projectiles.
Predictably, recovery skill also increases as level increases. Low level CPUs tend to recover predictably (if at all), using up smashes and fairly linear, predictable recoveries. Contrarily, higher level CPUs may try to combo attacks to recover (for example, I have observed a level 9 Mario try to use his cape to gain some horizontal recovery before using his Super Jump Punch).
The differences between CPU Levels is based on an illusion of added skill, by allowing the AI to both react quicker, and follow through with decisions faster as their level increases. This results in improved attacking, shielding, and dodging, as well as more advanced recovery techniques for higher level CPUs.