Around September 29, 2010, people started reporting that their sent transactions would not confirm. This happened because people modified Bitcoin to send sub-0.01 transactions without any fees. A 0.01 fee was at that time required by the network for such transactions (essentially prohibiting them), so the transactions remained at 0 confirmations forever. This became a more serious issue because Bitcoin would send transactions using bitcoins gotten from transactions with 0 confirmations, and these resulting transactions would also never confirm. Because Bitcoin tends to prefer sending smaller coins, these invalid transactions quickly multiplied, contaminating the wallets of everyone who received them.
Bitcoin was changed to only select coins with at least 1 confirmation. The remaining sub-0.01 transactions were cleared by generators who modified their version of Bitcoin to not require the micropayment fee. It took a while for everything to get cleared, though, because many of the intermediate transactions had been forgotten by the network by this point and had to be rebroadcast by the original senders.
On August 15 2010, it was discovered that block 74638 contained a transaction that created over 184 billion bitcoins for two different addresses. This was possible because the code used for checking transactions before including them in a block didn't account for the case of outputs so large that they overflowed when summed. A new version was published within a few hours of the discovery. The block chain had to be forked. Although many unpatched nodes continued to build on the "bad" block chain, the "good" block chain overtook it at a block height of 74691. The bad transaction no longer exists for people using the longest chain.
The block and transaction:
CBlock(hash=0000000000790ab3, ver=1, hashPrevBlock=0000000000606865, hashMerkleRoot=618eba, nTime=1281891957, nBits=1c00800e, nNonce=28192719, vtx=2) CTransaction(hash=012cd8, ver=1, vin.size=1, vout.size=1, nLockTime=0) CTxIn(COutPoint(000000, -1), coinbase 040e80001c028f00) CTxOut(nValue=50.51000000, scriptPubKey=0x4F4BA55D1580F8C3A8A2C7) CTransaction(hash=1d5e51, ver=1, vin.size=1, vout.size=2, nLockTime=0) CTxIn(COutPoint(237fe8, 0), scriptSig=0xA87C02384E1F184B79C6AC) CTxOut(nValue=92233720368.54275808, scriptPubKey=OP_DUP OP_HASH160 0xB7A7) CTxOut(nValue=92233720368.54275808, scriptPubKey=OP_DUP OP_HASH160 0x1512) vMerkleTree: 012cd8 1d5e51 618eba Block hash: 0000000000790ab3f22ec756ad43b6ab569abf0bddeb97c67a6f7b1470a7ec1c Transaction hash: 1d5e512a9723cbef373b970eb52f1e9598ad67e7408077a82fdac194b65333c9
On July 29 2010, it was discovered that block 71036 contained several transactions with a ton of OP_CHECKSIG commands. There should only ever be one such command. This caused every node to do extra unnecessary work, and it could have been used as a denial-of-service attack. A new version of Bitcoin was quickly released. The new version did not cause a fork on the main network, though it did cause one on the test network (where someone had played around with the attack more).
LSHIFT and RETURN bugs
On July 28 2010 two bugs were discovered and demonstrated on the test network. The first caused bitcoin to crash on some machines when processing a transaction containing an OP_LSHIFT. The second exploited another bug in the transaction handling code and allowed an attacker to spend coins that they did not own. Neither were exploited on the main network, and both were fixed by Bitcoin version 0.3.5.
After these bugs were discovered, many currently-unused script words were disabled for safety.
ASCII embedding into blockchain
Security researchers Dan Kaminski and Travis Goodspeed successfully embedded extraneous text into the blockchain from a mined block. This was disclosed on July 31, 2011 -- days prior to Kaminski's presentation at the BlackHat hacker conference in which Kaminski will discuss "BitCoin: Network Manipulation for Fun And (Literal) Profit".
This "attack" is harmless and has been known forever. It was used to insert a message into the genesis block.