This is a recurring question. So, instead of repeating it over and over, just point people to this editorial.

One-line summaries tend to radicalise people, but let's try anyway: great techs, great devs, great recognition.

CryptoNote

It uses CryptoNote technology, which, compared to most other coins, means:

• higher privacy if implemented correctly (ring signature + stealth addresses).
• higher scalability (no fixed limit, including the infamous 1MB blocksize, very high efficiency of the ed255199 signature scheme)
• higher security (the Curve25519 is considered safe by cryptographers, contrary to secp256k1
• changes are so fundamental that the adage "whatever coin X can do, Bitcoin can add it" doesn't apply here
• emulates bank secrecy on demand and permits regulatory compliance (view key - see Monero, the Next Step, slide 9)
• enforces net neutrality by design (miners cannot become censors, Wikileaks cannot have its donations delayed and a competitor cannot hinders payments to your company)
• smooth emission curve (no block halving here)
• GPU-resistance (GPU are only slightly faster than CPU). CryptoNight is said to be "memory hard" or "AES heavy"
• Code for wallet is separated from code for node, which is more secure

Remarks:

• Some altcoins exhibit one technology that Monero has: Shadowcash has cryptonote-like privacy (but only on exceptional situation called Shadow-to-Shadow), Vertcoin and some others have stealth addresses, etc.
• Improper implementation could lead to no actual privacy. Best example is Bytecoin, where 80%+ of the outputs are owned by unknown parties; so unmasking which signature in a ring is the real one is trivial for the said unknown parties.
• More technical information on CryptoNote: https://bitcointalk.org/index.php?topic=975984.msg10663673#msg10663673

Leader

The undisputed leader in Cryptonote-based coins:

• highest volume and good liquidity
• highest marketcap
• most active team
  • two public faces: David Latapie and Riccardo Spagni
  • several academic cryptographers
• largest community
• largest recognition
• fair distribution (devtome-sanctionned)
• smooth emission curve (no block halving here)
• best candidate for the catastrophic niche hedge scenario

Specific development

Monero has its own improvements that other CryptoNote-based coins ("altnotes") do not have:

• the only truly fungible cryptocurrency (Bitcoin is not fungible enough, Zerocash doesn't exist and since 82% of Bytecoin is owned by some unknown parties, fungibility cannot be achieved)
• a vision: the Three Pillars of Monero
• mnemonic seed (compared to Electrum's mnemonic seeds, they are also typo-resistant and usable on non-SPV wallets)
• per-kb transaction fees (Bitcoin has it too starting from 0.10, but Bitcoin is not a CryptoNote)
• tail emission to protect against the lack of ultimate incentives to secure the network
• mandatory minimum mixin with proper dust-cleaning
• OpenAlias (now possible with Electrum too)
• IP protection with i2p C++ router (partnership with Privacy Solutions, 80% done, why we chose i2p over Tor)
• FreeBSD port, Raspberry soon to come
• URS (not implemented yet)
• Much more to come

Read more

• Why Monero Matters
• Spec Chart for Major Cryptos, Monero edition
• Some other editorials: Letter to an investor, The Value of Privacy