I don't really understand what is so good about Protoss Motherships. They call them the "ultimate Protoss unit", but when I built one, it wasn't very good. I understand that they can teleport units, but other than that, what can they do?
The mothership has three abilities;
Mass Recall as you listed is probably the least interesting ability. It instantly transports a chunk of units to the mothership's position. This can be used offensively to reinforce your army from your production base or defensively to pull out units from a losing battle.
Vortex is the other active ability and is much more interesting. Akin to the "Stasis Field" from the Arbiter, a Starcraft 1 unit of which the mothership was derived from, this takes any group of units in the field out of the battle for a little while. This too can be used both offensively and defensively.
On the offensive this ability really shines, you can remove half of your opponents army from the battle, allowing your army to dominate the remaining forces by outnumbering them. When the vortex ends, the remaining army of your opponent's pops out and you can finish them off. This can also be used to remove problematic units from the battlefield such as sieged tanks.
Defensively, you can protect your own units from a losing battle while reinforcements arrive.
Cloak is the passive ability of the mothership. It renders all friendly (including allied) units and buildings invisible (and untargetable) unless detected with a detector. If your opponent did not expect you to bring cloaked units, it forces them to fall back or take heavy losses from your invisible army. Only the mothership remains visible, however the range of cloak is quite significant.
Overall, the mothership is an interesting option for late game protoss. However, you should only consider building one if your opponent is lacking detection or anti-air.
You can also do a mothership rush:
Finally, the "ultimate unit" is a disputable claim on the tooltip, as the mothership is being removed in the next expansion, Heart of the Swarm.
The Mothership is a very effective unit, however, it is rarely used due to being late-game unit and being very expensive (and time consuming) to produce. However, when it is produced, and when it is used correctly, it is an immensely powerful unit.
Cloak will cloak all your units within 5 units of the Mothership. This is a very useful ability for both offense, and defense, especially against Terran. Unlock Protoss and Zerg, which can rely on observers and overseers for detections, Terrans rely mostly on scans (Ravens can be used as well, but they in late game it's fairly easy for a Protoss player to pick them off).
Vortex allows you to remove units from the battlefield for a short period of time, which can be used to protect your own units against AOE attacks or when you're outnumbered and waiting for reinforcements.
Vortex also an be used to reduce the size of the enemies army, giving you an advantage in battle, and also remove key threats from your enemies forces until you can reduce the size of their army so they are easier to deal with. Both of these can also be accomplished by a Sentry's force field and a Phoenix's Graviaton beam, but has the advantage of being able to affect all units instead of just certain types of units.
Mass Recall allows you to teleport your army to your mothership. When used correctly it can be the the most useful ability offered by the Mothership. Although it can be used for defense, calling your army back to your base when under attack, it is most useful when used offensively. This is because Mass Recall will allow you to perform very effective hit and run attacks against your opponent, dealing considerable damage to their base at little cost and risk to yourself. Since you can pull your army away at a moments notice this allows you to quickly react to either your opponent attacking you at his base, or attacking you at your own base. In both cases you can simply teleport your army away to either avoid them taking damage, or defend your base before your opponent has time to deal any significant damage. If your enemy has a large base (very likely considering the MOthership is a late game unit), it can also allow you to attack one half of the enemies base and then mass recall your army to to the other half once your opponents army has been taken out of position.
This video shows some excellent Mothership play by Kiwikaki in Game 2 vs stephano at IPL 3:
Well first of all try not to get attached to it since it will be gone in HotS. I don't have time for a detailed analysis, but I see someone else already provided that. What I can say is that in very long games, as protoss you try to do one thing (besides winning). That thing is: get the absolute best unit composition possible.
Now how does this work. You start off with stalker, zealot, sentry. Maybe immortal or HT. Later you evolve to Colossus, and at some point around min 25 or so you're on 4-5 bases (even if the 5th is just a gass base).
You have to slowly transition out of tier 1 and 2 units. You will stop making zealots and stalkers, instead you want 5 Colossi (more than 5 is just a waste since 9 Colossi accomplish just as much as 5-6). You will want some immortals to soak up some damage and A LOT OF ARCHONS. maybe some blink stalkers, they are very good, but not too many unless your opponent is zerg and going for brood lords (void rays are better but mineral and gass requirements make it hard).
With this perfect army you can crush most of anything, but if cought out of position YOU CAN STILL LOSE. So you want a "Oh crap button" (note: can be used as a FU button also). That button is the vortex.
While yest the cloak field punishes any opponent that doesn't have enough detection, the vortex is what you want. Once you place a good vortex, just plop all archons inside (called an archon toilet) and position colossi in range of vortex.
When units come out of the vortex they are 100% clumped up (so any splash will hit all units) and the AI attacks the very moment they come out. Since both colossi AND archon have 100% splash (tanks for example do not) you will MURDER anything inside.
That is all, GL & HF :)