Essential Tools

Chain Checker: as cassettes have gone from eight speeds to nine, ten and eleven, chains and cogsets have become increasingly expensive. So improperly judging wear on these parts carries painful financial consequences. With a chain checker, you can accurately gauge your chain's life in real terms so you don't toss one that still has miles to go -- and you don't keep using one so worn that it starts eating your cassette cogs alive.
Floor Pump: Which one to get? It is good to pump up your tires before every ride, keeping them near the recommended pressure. The Park floor pump works for both Presta and Schrader valves and easily pumps tires to 160 psi.
Minipump: As minipumps go, you can't get bigger dependability than the Blackburn Airstick. It's not the most expensive model, nor the lightest available. But its durable, ideal for the roadside or trail. Set it to high volume to fill tires quickly to about 80psi; when the pumping gets tough, flip a switch into high-pressure mode and inflate up to 130psi.
Chain Tool: these come in many varieties, from compact, budget models that simply get the job done to gorgeous, lust-worthy pieces of art that make every chain replacement feel like a sacred ritual. The Park CT-5 is a nice simple chain tool that gets the job done without breaking the bank.
Tire Levers: If you have a hard time getting tires off the rim, try Pedro's tire levers. Their broad, flat blade and rigid plastic build make them kind to tires and rims and just as effective on stubborn ones.
Cable Cutter: The Park cable cutters work perfectly to cut both cables and housing with ease and they are a good tool to have at home for any zip tie and wire cutting needs.
Hex Keys: of the hand tools that are a necessity for every cyclist, first and most obvious are these. (Many people call them by the brand name, Allen.) Bicycle-specific toolmakers make sets, but quality metric keys from a hardware store work fine. Get the following sizes: 1.5-, 2-, 2.5-, 3-, 4-, 5-, 6-, 8- and 10mm. These will work with tiny setscrews on suspension-fork adjuster knobs, crankarm fixing bolts and everything else.
Multitool: a good multitool can mean the difference between making a swift, easy midride adjustment and hobbling home with a scowl. Always carry a palm-sized workshop like the Park IB-3, which has several sizes of hex keys, a chain tool, as well as both a Philips and flathead screwdrivers.
Spoke Wrenches: with so many wheel manufacturers using unique spoke-nipple designs, it's impossible to recommend any one model. If you have conventional square spoke nipples on your wheels, you can't go wrong with Park Tool's SW-0, SW-1, or SW-2. The design has hardly changed since the 1960s -- and that's because it doesn't need changing.

Looking for more information? Check out these articles:
DIY: Repair, Reuse, Recycle
Park Tool Tips
Housing and Cables
Chain