Finding runes, especially higher level runes, is an obsession for many players. This can be a chore, since there's no way to use equipment to increase your odds of finding more runes, or higher level runes. Magic Find has no effect on rune drops, either quality or quantity; the way to find runes is to kill lots of monsters in larger games, so more total items drop.

Quests

Several quests grant runes as part of their reward.

Forgotten Tower

This quest does not have a Rune as part of its reward (just a bunch of gold and minor items from a magical chest), but since v1.09 The Countess, a SuperUnique Corrupt Rogue you must kill to accomplish the quest, has begun dropping a rune almost every time she's killed. Her rune drops were increased still further in v1.10, and she's now a very popular target for item running characters.

Which runes she can drop vary by difficulty level.

Normal: El (r01) - Ral (r08).
Nightmare: El (r01) - Io/Ko (r18); above Io (r16) is much rarer.
Hell: El (r01) - Ist/Lo (r28); above Ist (r26) is much rarer.

The Countess has better odds to drop a higher level rune the first time a player kills her on Nightmare or Hell difficulties, when they get credit for completing the quest. This is reflected in the different odds for Io/Ko and Ist/Lo listed above. Her odds of dropping her highest possible runes are always astronomical, but they are slightly better the first time than the other times.

She is capable of dropping up to six runes each death, and will often drop two or three. They're very unlikely to be higher than Tir or Eth, but reports of two Hels, and a couple of other mid-level runes are not uncommon, so it's possible.

The Hellforge

When a character shatters Mephisto's Soulstone on the Hellforge in Act Four, four gems and one rune drop as part of the quest reward. The runes that may be found from this quest vary by difficulty level. Which one drops is selected randomly from the following possibilities:

Normal: El (r01) - Amn (r11).
Nightmare: Sol (r12) - Um (r22).
Hell: Hel (r15) - Gul (r25).

Unlike the runes from The Countess, or any other monster drops in the game, the lower level runes are not more common. The odds for Hel or Gul are identical on Hell, 1/11 for each. Cross your fingers.

Be sure to complete this quest when you can get your rune drop, and do not finish it with other players in your party, if they have not finished the quest already. Four gems drop for every character completing the quest, whether they're near the Hellforge or not, but only one rune will drop for the quest completion, whether one or eight characters are in the party/completing the quest.

Rescue on Mount Arreats

This second quest in Act Five is easily accomplished, and your character will receive a Tal (r07), a Ral (r08), and an Ort (r09) rune as a reward for completing it. Not a huge reward, but for players who save all their runes to upgrade, every one helps.

Chests

Chests (this includes barrels, crates, hidden stashes, etc) are an excellent source of items, including runes. The level that chests drop at is determined by the area of the game they're found on; consult the Levels section for that information. The level of runes that can be found from chests progresses steadily as you move through the game.

The following list details the highest level runes you can find in any area. All of the lower level runes may also be found there, and in fact are far more likely to appear than the higher level ones.

Act 1 Normal: No Runes from Chests
Act 2 Normal: El/Eld/Tir/Nef (r01-r04)
Act 3 Normal: Eth/Ith/Tal/Ral (r05-r08)
Act 4 Normal: Ort/Thul/Amn/Sol (r09-r12)
Act 5 Normal: Shael/Dol (r13-r14)
Act 1 Nightmare: Hel/Io (r15-r16)
Act 2 Nightmare: Lum/Ko (r17-r18)
Act 3 Nightmare: Fal/Lem (r19-r20)
Act 4 Nightmare: Pul/Um (r21-r22)
Act 5 Nightmare: Mal/Ist (r23-r24)
Act 1 Hell: Gul/Vex (r25-r26)
Act 2 Hell: Ohm/Lo (r27-r28)
Act 3 Hell: Sur/Ber (r29-r30)
Act 4 Hell: Jah/Cham (r31-r32)
Act 5 Hell: Zod (r33)

Upgrading

Prior to v1.10, it was hit or miss obtaining runes above Ort, since only the first nine runes could be upgraded in the Horadric Cube. This changed in v1.10, when rune upgrade recipes were added that could turn Els into a Zod. That would take several million Els, but it's now possible to upgrade to all levels of runes, which makes collecting and building towards the high level runes the biggest Runewords require a possibility for all patient players.