During the Wolf-359 incident, 39 starships were destroyed, and 11,000 people were killed or assimilated.
Why didn’t one of the smaller ships warp into that one Borg cube? Doesn’t warping into it destroy anything?
Even if it just warps through without touching, one could program the navicom to self destruct while the ship is in the middle of Borg cube.
Trivial, really: The Federation is simply not in the business of Kamikaze suicide runs. And since we haven't seen an entire space-ship piloted per remote in a very reliable manner (not even shuttles), that's exactly what it would have to be.
If they dispatch a fleet of 39 ships to apprehend the Borg, they might not be surprised of casualties, but having a ship's crew sacrifice themselves is so horribly incompatible with the spirit of Star Trek (i.e. out-of-universe) and the Federation (in-universe) that Roddenberry'd be spinning like a drill in his grave for the mere suggestion.
Having said that, a similar tactic (at impulse speed, not at warp) was used once by Chakotay to take out a Kazon ship, but he had to be beamed out very dramatically milliseconds before impact, so the Kazon couldn't shoot the projectile ship down before impact. Now, this was close to impossible to do to a primitive Kazon ship (a species so primitive the Borg didn't even bother to assimilate). Think about how hard such a manoeuvre would be to use against the Borg.
The "technical challenges" of this maneuver seem trivial to me given the facts: starships have ultra advanced computers and seemingly perfect warp timing capabilities (if you can recall the VOY episode where they burst-warp through a maze of obstacles). Shuttles or even ships can be piloted by a single person or remotely if need be, minimizing loss of life. Borg cubes are not the most agile of ships, I doubt one has the ability to move out of the way fast enough to dodge a vessel at warp, while simultaneously engaged in combat with other ships, and finally, one would only need to engage warp from a distance just outside the cube's weapons range... or maybe even within it. The cube could anticipate the move by scanning the ship you say, well then do it with a cloaked ship. Why not warp into a cube from right next to the cube? Maybe you'd choose to be further away just to "build up more speed". Overall it seems like a cube is a target that's hard to miss, and that doing this might be well justified if the cube has already taken out 38 of your ships with no signs of stopping.
I present an alternate "explanation" as to why we've never seen this rockin' awesome maneuver:
Could it be that the materials starships are constructed from have a strength-to-weight ratio that is so high that the inertia of a starship collision would actually do little damage, even at warp speed, as compared with the starship's weapons and warp core detonation?
or... OR... that the fake laws of physics dictate that a ship at warp actually has very little inertia... somehow.
The problem is that by the time a star ship is so badly damaged that there is no possible hope for it and the best move is to sacrifice everyone on board for chance of doing some damage to the cube then the ship is normally too badly damaged to actually go fast enough and survive enough shots to actually ram the cube in the first place.
As for an unmanned shuttle it would need to move extremely fast in an evasive way to reach the cube. The faster you go the more your mistakes matter, imagine travelling at the speed of light and being one degree out. This means that your programming would have to be absolutely perfect even though you would not be able to reliably determine where the cube was going to be in relation to yourself (assuming the craft was launched from your ship). If you get all that right then it only takes the cube to get a good shot in (even if it misses it can knock you off course) or the cube to move slightly and it is all for nothing. Even if you hit it then it still might not do a significant amount of damage.
Although, I am not aware of anyone ever saying in universe that they had never done this.
Simple: let us say, hypothetically, that you think the earth is about to be assimilated. You are the captain of a starship in the midst of the battle, and you realize the billions of lives on earth are more important than the hundreds on board your vessel. You have two logical reasons not to make a suicide run:
1.) You still think you have a chane to win without destroying your own ship.
2.) Your ship is damaged, and you cannot make a suicide run.
(3. A suicide run is so against your idealogy you'll doom billions so your crew can have somebody else kill them slightly later - not a logical reason.)
We know that the Borg, if you've ever seen First Contact, do not concentrate their fire on just one enemy ship to destroy, so by the time a kamikaze attack seemed like a good idea, it was probably too late for that judgement call to be made - none of the battered vessels left intact were capable of warp.
You'll notice that as Acting Captain, Commander Riker did order a collision at warp two that was belayed at the last possible moment.
A warp bubble does not impart any additional force, the bubble bends space so you are not technically moving at all, instead space is.
Basic physics says it would takes the entire power of the universe (infinite energy) to reach light speed, so there is no way the warp core does that. If it did any warp factor above 1 would have to destroy the universe if it imparted that energy to the target - so it can't work like that. Its been stated that the bubble moves space not the ship, so a ship at warp would be no different than one at max impulse (its not moving any faster than it was)
There is no way to reconcile the problem if at warp you release enough power to destroy the entire universe (and multiple times over above warp 1), so it can't be transferring momentum into energy
The same effect would have to be present for a warp core breach too, if that's how it worked but it isn't, one warp core goes bang so does the universe (as it would need to produce enough energy to cross the light barrier, which we know it doesn't), so it cannot work that way. Therefore the only conclusion is that ramming a ship is no different than a torpedo (its the detonation not the impact at warp that does the damage), ramming at impulse makes sense though as you get the impact and detonation
Bottom line is that warp does not (can not) travel faster than light from a momentum point of view
You could not warp into a ship. Warp Drive Involves surrounding the ship in an artificial Bubble of time space to avoid all those pesky issues that happen to objects traveling faster than the speed of light. Hence you cannot run in to anything much less ram anything.
How do we know that none were attempted? No (canonical) record of what happened to all the ships is available, other than they were destroyed. For all we know, one tried a ram and was unsuccessful. If it is a "desperate tactic" that Starfleet uses (or even one that Picard himself would consider), presumably the Borg would have prepared for it. (This is prior to the Voyager retcon of the power, anyway.)
James Jenkins' speculations are closer to reasonable.
However, the real reason they didn't warp into the cube is because if they did there would've been no rest of the movie. The writers didn't think that deeply into it. Obviously. I mean, come on. The plot revolves around the Borg going back in time.
Engag...but was interrupted by data.