There are actually 3 conditions that need to be met for somebody to join your party.
1. The total number of party members must not exceed your level. (In the NES version, the criterion is slightly different; the number of companions you have recruited can't exceed your level, so you only need to be level 7 to get everyone, or 3 to get a full party of 4. Then again, the NES version doesn't require everyone to be in your party to beat the game)
2. You can't recruit the character of your own class.
3. If your virtue (in the corresponding virtue) is too low, the corresponding companion will not join your party. (In the NES version, this criterion is also checked when picking up a character from the hostel.)
Criterion 3 hasn't been mentioned before in this topic, so I figure I would mention it here. For example, if you go to Moonglow, cheat the reagent seller several times, then try to get Mariah to join, it is likely that she will refuse. (For good measure, you could steal the chest in front of her before asking her to join.)
HiPhish: Your party size cannot exceed your own character level. This means on level 1 you have to travel alone, on level 2 you can have one companions, on level 3 up to two and so on until level 8. You also cannot get the companions who has the same class as you have (for example, if you were a bard Iolo wouldn't join you).
Some advice while I'm at it: don't take as many companions as you can, about three companions is good. If you have a larger party the game gets much slower because everyone has to take their turn. Plus levelling them all up takes forever.
However, to beat the game you will need a full party. I recommend holding off on them until you are ready for the final dungeon. Then get them, enter the dungeon and let them get killed. They will still be in your party but won't be taking turns. Make sure to revive them before entering the last rooms, so keep enough revive spells handy. Actually, i don't know if they need to be live or not, but after making it through eight levels of the Abyss I didn't want to risk being thrown out again.
One other recommendation: The ideal 3 person party for endgame is Mage, Bard, Druid because those 3 classes are the only ones that can equip the Magic Wand, the best weapon in the game. (Mystic Sword is stronger but is only a melee weapon, so it isn't as good; you are better off selling them (not all at once because of the 9999 gold cap) to get money for more Magic Wands.)