Amendment

No doubts that SpellCatcher, as others mentioned here, is the most recommended app for this situation. It's integration w/the system, plus advanced capabilities has no contenders yet.

CopyPaste does much of what Spell Catcher can do by the sounds of it, plus it's main feature of keeping track of the last 20 items that you copied, so that you can re-paste things. And it does auto-complete of long words.

http://www.copypaste-x.com/

Spell-checkers are useful, but they only catch misspellings that aren't other words. Due ewe no watt eye mean?

I'm with Brian Ashe. Anytime I'm typing anything anywhere with OS X, if something is misspelled it gets underlined in red. Select the questionable spelling, control-click on the selection, and you get a very convenient context-sensitve menu with known corrections, spelling controls, and a host of other very handy options. It's all you need!

Start typing a word in a cocoa app textfield and hit the esc key. You will see an autocomplete come up - much simpler!

Another massive fan of Spell Catcher. Once you try it, there's always jaw-dropping moment when you realize how slick and well-integrated it is. For instance, if I misspell some word, such as ... mispell ... It actually automatically corrects the word the second I put that space afterwards. This is because it's a common word for me to misspell, so I entered that into my autocorrects (which is all done via keyboard shortcuts). Even better: if I misspell an odd word, like "industrous" ... Spell Catcher brings up a small window that has up to 10 possible corrections. Here's the kicker: aside each word is a number. Hit that number and Spell Catcher quickly replaces the bad word with the good one.

It doesn't stop there: it also has an optional Ghost Writer, which records every lettered keystroke in your choice of apps, in a dated basic text file. If you write a lot, and suddenly trash some doc you made last week that you were supposed to keep, no worries. It's there in a text doc. These text docs can be automatically deleted after XX amount of days, so you don't end up with thousands of files. Just a few weeks, or a couple months, whatever you want.

It's truly the first program I reinstall onto my new Macs when I first get them.

It will work in Mail and Pages when the final version is released; they use webkit and not NSTextView or whatever, but that capability is currently being added.

c.f. their website

Can't let this pass without mentioning the granddaddy of all spellcheckers, Spellcatcher (Formerlly "Thunder"). Amendment might execute the pop-up a little differently, but Spellcatcher has been doing that for years. And the pop-up is a choice, I use the audible signal.
http://www.spellcatcher.com/

I'm the author of a simple, system-wide Spellchecker for Mac OS X called HyperSpell. HyperSpell lets you check spelling from any application, not just certain Cocoa applications. HyperSpell can be driven completely from the keyboard allowing you to quickly check spelling from any application.

If Amendment is something you might like then you should also check out HyperSpell, it's only $10:

http://kuwan.net/hyperspell

doesnt safari give you a built in spellchecker? whats wrong with that?