I have soloed BG1 with a Dwarven Berserker (without reloading) several times during the course of the No-Reload challenge, as reported on the old BG1 bioware forums (no longer available).
IMO this is one of the easiest characters that you can solo BG1 with. With Enrage they are immune to any disabling spells (charm, sleep, stun, hold, etc.) that an enemy mage, siren, ghast, or ghoul might throw at you. They thus make awesome caster killers. Being able to wear good armor and weild a shield, also makes them good tanks against ranged and melee enemies. So, basically, they can just charge in and decimate the opposition, with little fear. Their relatively high hit points also keeps them safe against the few traps that they must run through to complete the game.
I have tried to no-reload a berserker through BG2 on two separate occassions, but failed against improved Draconis/Abazigal (Ascension + SCS2) on both attempts. There has been at least one successful victory (not by me) of an unkitted fighter over improved Melissan (Ascension) on INSANE! But that took many, many reloads.
A plain un-kitted fighter is much more difficult in both BG1 and BG2, because they are vulnerable to a whole range of disabling spells, and must play more cautiously and reliantly upon potions and items for protection.