How has (almost) nobody mentioned dual-classing yet? Bringing one class up until it switches to a linear xp progression and flat hp gains instead of hit dice, then switching to another class can often be helpful. Plus, it's straight out of the PHB and works for both 1st and 2nd edition. It does rely on high stats (at least one 15 and one 17), but if you can meet them it's fairly awesome. Baldur's Gate and Icewind Dale have good character generation systems for this, and I've had good results using dual-classed characters in IWD. The old gold box games from when TSR still did D&D made it easy to make your stats (just set everything to 18), but the way it forced you up to a specific xp total immediately made it hard to dual class properly.
Good Fighter breakpoints include 7th level (3/2 attacks/round), 9th level (7th weapon proficiency, 9th HD, 250k xp), 13th level (2 attacks/round, 8 weapon proficiencies, 9 HD + 12 hp, THaC0 8, 1.25 million xp). I'm not a huge fan of 13th because of the high xp cost, which usually costs 3-5 levels of whatever you dual class into. Fighters are bad to go into due to their lack of higher end abilities, although 2nd edition single-classed fighters were still nice.
Thieves are usually better to go into than out of due to their poor HD. Good breakpoints include 5th (3 weapon proficiencies, x3 backstab, 1-2 thieving skills maxed out), 10th level (x4 backstab, 2-4 skills maxed, 75% scroll use), and whenever else you manage to max out another skill or improve your backstab multiplier. Usually I find them better to go into due to their lower initial HD and higher level for a given xp value. At 220k xp/level and +2 hp/level, thieves actually get about 76% of the hp per xp that a fighter would get (after 9th level, of course).
Clerics are similar to thieves and wizards with respect to going into them. The loss of edged weapons is usually a pain due to the prevalence of magical longswords, but not that bad otherwise with an accommodating DM. High end spells aren't bad, and you can cast fully in armor. At only 225k xp/level past 9th level, they grow in hp almost as fast as thieves. Faster if you include the benefit of their healing and buff spells. Add in a batter THaC0 progression and you have a strong class to dual into from fighter (weapons not withstanding).
Wizards are horrible coming out of, but wonderful coming into. A whatever//Wizard gets better HD and various other goodies from the initial class, skips the wizard's pathetic early levels, and only costs a small amount of high end spellcasting as compensation. High xp classes usually aren't as good to dual into because it delays regaining your class features, but wizard is worth it because of all you gain from another class, any other class.
A Fighter 9//Wizard X costs 250k xp (less than a single additional level of Wizard) in exchange for 7 weapon proficiencies, the ability to wear armor (elven chainmail allows casting and has a decent AC, only 2 less than platemail or 4 less than full plate), exceptional strength (not too important with belts of giant strength, but still worth mentioning), efficient hp gains from HD (full +4 or better Constitution bonus to HP for the first 9 levels of d10, then another 2 levels of d4+2 in 1st edition, then the usual Wizard +1 hp/level), 3/2 attacks per round (before weapon specialization, haste, tenser's transformation, and anything else), and probably a few other goodies I can't think of. At the low levels, you're a fighter instead of a squishy wizard with d4 hp and 1 spell/day. At the high levels you're a wizard with extra hp, AC, combat ability (if you need to gish it up) at the cost of only one or two high level spells/day. Heck, 23% of the time (250k xp lost out of 325k xp per additional wizard level) you're at the same level as the full wizard, anyways.
Other good combos include Fighter//Thief (backstab with high attacks/round and easy exceptional strength to multiply), Thief//Wizard (skip the bad early wizard parts, use elven chainmail, thief skills mean you don't need Knock and can use some scrolls you might otherwise not due to specialization), and Ranger 9//Cleric (IWD only, gives Druid spell access on Cleric side, dual-wielding, all of the usual Fighter 9 goodies with only 50k more xp spent). Cleric 9 or 14//Wizard might also be worth looking into for similar reasons as the Ranger//Cleric in Icewind Dale (casting from multiple lists, armor, good hp).