- A Dwarf Fighter/Thief is limited to Fighter 7 unless they have high Strength. They reach that cap at 250,000 XP as a Fighter 7/Thief 9 -- equivalent to a Human 9th level Fighter. Compared to the Human, the Dwarf is already a noticeably weaker combatant, with 35 HP rather than 49, +6 to hit rather than +8, and no free castle or army. His level-based saves have suffered: 10/12/11/10/11 instead of 10/9/8/9/11. However, being a Dwarf will give him an average of +3 to save against spells, wands, and poison, which basically makes up for it. In exchange for these numerical disadvantages, he gets Thief skills, Darkvision, and some random bullshit +1 racial enmity bonuses and free languages. It's a trade-off, but a very favorable one in my mind. It's worth noting that few games will ever progress substantially past here.
What happens if we do? Well, when the single-classed Thief finally hits level 13, he'll have better HP and Saves, and equivalent attack bonuses to the Fighter/Thief, making him basically strictly better. However, that doesn't happen until 660,000 XP, which is a long, long way away. A Human Fighter will fairly rapidly get MUCH better HP and saves than the Dwarf, but won't deal substantially more damage in combat until level 13 (1,250,000 XP!). The Dwarf will still have darkvision, thief skills, and access to awesome dwarf-only magic items, and will have acquired a thieve's guild, so even then it's not clear which character is better. Conclusion: A Dwarf Thief eventually becomes almost strictly superior to a Fighter/Thief around 660K, while a Human Fighter continues to fight better but lack thievery-- the same dynamic as before the level cap. - An Elf Fighter/Magic User caps out as Fighter5/Magic-User 5, when a Human could have been Fighter 6 and an elf or human could be... Magic-User 5. Since Fighters don't even get save progression at 6, it's pretty clear that the multiclass is way better at this point. Unfortunately, life goes downhill pretty quickly. A Human Fighter will hit 7 and get +50% attack speed while the Elf is still 5/5. At this point it's starting to look bad for the Elf, but it's nothing casting Protection from Evil, Strength, and Mirror Image won't fix. Not to mention a racial +1 hit, stealth, and darkvision. The human will hit Fighter 9 for massive HP, saves, and followers when the Elf is 5/8, at which point the Elf should probably give up on trying to compete in melee and console themselves with being an armored caster laying down 4th-level spells. The Elf caps out altogether at Fighter5/Magic-User 9 with 270,000XP, compare Fighter 9 or Magic-user 10. At this point the F/MU is basically trading a few spell slots for armor, darkvision, and charm immunity, which seems well worth it. A Human Magic-User doesn't get higher-level spells than the Elf until level 12 (750,000XP) and even then it's debatable who's better. Conclusion: an Elf Fighter/Magic-User is a credible Fighter until around 250K and a credible caster until 750K.
- Since you're getting the idea, let's do an Elf Magic-User/Thief real quick. They don't cap until Magic-User 9/Thief 11 at 270k, at which time they have basically everything good from both classes. They don't fall behind a spell level until 750K, when a Human Magic-User 12 throws down 6th-level spells and enjoys better saves, while the Elf Magic-User 9/Thief 11 throws down 5th-level spells from stealth, in the dark.Conclusion: An Elf Magic-User/Thief remains viable essentially forever
- An Elf Fighter/Magic-User/Thief doesn't cap anything until 54K, doesn't cap both until 405K, as a Fighter5/Magic-User 9/Thief9. Conclusion: this character kind of sucks, but because of dividing XP, not because of level limits.
- Half-Elves mostly suck compared to real Elves, but they do have the option to splash Cleric. A Half-Elf Mage/Cleric starts sucking as a cleric pretty fast, falling behind by a spell level as early as 55K. So, they're really not so much a Cleric substitute as a Magic-User Variant. They cap out as Cleric5/Mage6, but being able to heal and cast spells in armor is good enough they don't start to feel bad about themselves until a human hits 5th-level spells at 135K. Throwing in Fighter for a triple-threat prevents you from capping out until 120K, although it doesn't actually extend your character's viability by much because Fighter 6 doesn't give you anything a Cleric 10 doesn't already have.
- Half-Elves also have the option to multiclass Ranger, which is OMGWTFBBQ good at low levels. However, they quickly cap out and become noticeably weak quite early. I mention them here only to note that if you are blessed with 17 Strength, you can hit Cleric5/Ranger7, which is a significant milestone that keeps you relevant for a much logner time.
- Halflings are technically allowed to be Fighters, but it's a trap. Just play a straight Thief.
- Gnomes cap out pretty fast, so aren't worth it in a long campaign unless you have a real hard-on for Illusionists.
- A Half-Orc Fighter/Assassin doesn't cap Fighter until 1MillionXP, and remains viable basically forever.
Longer Conclusions: Assuming PHB-only, no high stats and a very long campaign (1million+) I consider the following characters viable:
Dwarf: Fighter/Thief, Thief
Elf: Fighter/Magic-User, Magic-User/Thief,
Halfling: Thief
Gnome: Thief
Half-Elf: Cleric/Magic-User, Assassin
Half-Orc: Fighter/Assassin
Human: Fighter, Paladin, Ranger, Magic-User, Illusionist, Druid, Cleric, Monk
ETA: Also Human and Half-Elf Bards, of course--though if you have the stats to be one, you're cheating.
If we assume very high stats, some more characters get put on the table:
Elf: Fighter/Thief, Magic-User (displaces Human Magic-User)
Half-Elf: Fighter/Magic-User, Fighter/Magic-User/Cleric, Fighter/Magic-User/Thief
Gnome: Illusionist/Thief