There are some RPGs in which you can get monsters to join your party permanently (or, at least, until dismissed), and I am wondering what your preferred method of recruiting them.

Here are some that I have seen:
* In Pokemon, you recruit monsters by throwing special items called Poke Balls at them. This works best if the enemy is at low HP (but isn't an option if you've already killed the enemy), and there are also different varieties of Poke Ball, which have different prices and effectiveness. There's even a Master Ball, which always works, but (at least in 1st Gen) there's only one in the entire game (barring glitches, of course).
* Arc the Lad 2 has a character with a skill that's similar to Pokemon's Pokeballs; use it on an enemy and, especially if it's at low health (IIRC, could be wrong about this point), it may join your party permanently.
* In Dragon Quest 5 and 6 (SFC), a monster has a small chance of joining after a battle, with no way to manipulate it, provided you're of a high enough level (or, in DQ6, high enough rank in the monster tamer class).
* In Dragon Quest Monsters, a monster has a chance of joining, but you can increase the chance by feeding the monster meat during the fight. It is possible to get the chance up to 100%. (Note, however, that doing this with metal slime-type monsters is a bit risky, as there's the possibility that such monsters will run away even after being fed.)
* In some Shin Megami Tensei games (notably including the main series), a monster can be recruited by talking to it during battle and negotiating with it.
* In the Bard's Tale series, sometimes a monster will randomly offer to join your party. There's also a spell that forces an enemy into your party.
* There's also a few games with persistent summons, such as the Bard's Tale series (particularly classic versions of 2 and 3) and the Geneforge series. In these games, you use a summon spell or ability and the monster joins your party and stays at least until it dies (and in some cases, like Bard's Tale 2 and 3, perhaps even after death, in case you want to revive them).

(There may be other methods that I've forgotten, or that I am not aware of.)

So, what's your preferred method of recruiting enemy monsters into your party in RPGs where it's possible?

Dial number, get monster. This is in both Telefang games. If you know the number of the monster you want, just give it a call.

None of this capture/ask to join/tricksy hobbit nonsense.

This description reminds me of the Monster Rancher games, where one method to get a monster was to insert an arbitrary CD into the drive, and the game would generate a monster based off the data on the CD.

Being able to generate monsters from arbitrary telephone numbers (rather than just ones you obtain during the game) would be quite doable; just code a routine to generate the characteristics of the monster randomly, and use the phone number as a seed for the random number generator.

Dominate or charm spell, or defeat it to earn the summon. I like that.

Final Fantasy Tactics: One specific character class has a skill that's only function is to recruit enemies when it succeeds. After battle you can choose to keep or toss.

I like the Shin Megami Tensei(DS games) i've played, and how the monsters/etc(those you don't control) will react differently depending on if you have one of their species in your party or not(and if it's a certain time/moon phase).

I also like the geneforge series(I played bits of 1 and 2) as well.

Jade Cocoon: Play your flute and get a monster inside a cocoon. I like the tunes.

Usually permanent summons, but I guess the Pokemon method has its advantages, too, since it would feel more like an achievement and you might be able to recruit almost any monster in the game at will, instead of a few pre-selected summons. Talking to monsters sounds interesting too but it depends on how it's done.

The other methods seem too complicated or too random for my taste.

This sounds like it would either be spectacularly good or abysmal. How did it play? Ja, this was my only experience, though it's usually only temporary: Shadowrun, NwN.

Summoning/recruiting monsters is for filthy wizards. Go melee and give your enemies a taste of cold steel (or maybe silver if you're a Witcher).

None. All non human life forms with advanced cognitive processes must be eradicated.
The Human Hegemony will rule over all.

I'm not entirely sure they're random; but I've never researched the games too deeply.

I've never even played Pokemon, can you have more than 1 monster in your party during combat, or is it always a duel between 2 monsters?

Arcanum has persistent summons, in several flavors; the one that comes closest to what you're describing is the Familiar spell, which requires zero upkeep after casting.

It also has two conscription spells: Control Beast for creatures, and Dominate Will for sentient beings.

More to the point, thanks to an exploitable glitch in the game (commonly known as Meta abuse) those spells can be made permanent on as many people or creatures as you'd like. So while the game is set up to permit you around 6-8 followers at most, by using this exploit you can have dozens of them (to the point that the screen is so filled with their icons that even seeing what's going on around you becomes a bit of a challenge).

And since they level along with you, you could eventually find yourself the ringleader of a group that contains level 50 ailing wolves and beggars. Or the king of one of the cities you visit. Or random shopkeepers. Or even the in-game equivalent of Bigfoot.

It's a BBEG's wet dream.

In the earliest games, you could only have one pokemon out at a time, but you could, at the cost of a turn (or if your active pokemon faints), switch to a different pokemon. Wild pokemon battles only have you facing one enemy at a time, but enemy trainers can have multiple pokemon, and can swap between them just like you can (but an enemy swapping out a pokemon that hasn't fainted is extremely rare).

Later games in the series introduce double and even triple battles, where each side has 2 or even 3 pokemon out at once, but those tend to be the exception rather than the rule, I believe.

It's worth noting that, even with only one pokemon out at a time, the battle system still has a lot of depth, with lots of different pokemon moves and a pokemon type chart (for example, Grass > Water > Fire > Grass).