When the Germanic tribes known as the Anglo-Saxons and the Jutes arrived in the 5th century, the British Isles were a place of great linguistic diversity. Among the Celtic languages spoken there were the ancestors of the tongues now known as Irish, Scottish, Pictish, Breton, Welsh, Cornish, and Manx. It is a testiment to the linguistic imperialism of the English people that despite 1,500 years of assimilation, acculturation, conquest, and cohabitation so few words of Celtic origin have made their way into the English language. In fact, there are believed to be more words borrowed from Arabic than from all the insular Celtic languages combined. Here are the few Celtic loanwords that are in common English usage today (I have excluded words that only apply to Celtic culture, and the innumerable interesting but false folk etymologies that Celtophiles love to dream up):

From Irish (Gaelic):

banshee - bean síth, "woman of the fairy mound"
bard - bard, a high rank of poet
bog - bog, "soft"
brogue - bróg, "shoe"
drumlin - druim, "the ridge of a hill"
galore - go leór, "plenty, enough"
keen - caoin, "weep"
pet - peata, "a tame lamb"
phony - fàinne, "ring" (from the gilt brass ring used by swindlers)
shamrock - seamróg, "shamrock"
shanty - sean tigh, "old house"
slew - slúag, "army"
slob - slab, "mud"
slug - slug, "swollow"
smithereen - smidirin, diminutive of smiodar, "small fragment", i.e. "super small fragment"
Tory - tóraí, "robber, bandit"
whiskey - uisge beatha, "water of life"

From Scottish (Scots Gaelic):

cairn - càrn, "heap, pile"
clan - clann, "family, lineage"
claymore - claidheamh mór, "great sword"
crag - creagh, "rocky outcrop"
glen - gleann, "valley"
glom - glam, "grab, snatch"
hubbub - ubub, a Scottish exclamation of contempt
plaid - plaide, "blanket"
slogan - sluagh, "army" + ghairm, "call, shout"

From Welsh:

clutter - cludair, "heap, pile"
crumpet - crempog, "pancake, fritter"
flannel - gwlanen, "wool"
maggot - maceiod, "worms, grubs"
penguin - pen, "head" + gwyn, "white" (originally applied to the great auk)
tor - twr, "a rocky hill"
trousers - trews, "pants, trousers"
truant - truan, "wretched, miserable"

From Breton:

tan - tann, "oak"

From Cornish:

bludgeon - blugon, "mallet"
brill - brilli, "mackerel"
gull - gullan, "bird"