From http://desktoppub.about.com/cs/finetypography/ht/circumflex.htm
Under Windows hold down ALT while typing the appropriate number code on your numeric keypad to create characters with circumflex accent marks e.g. â 0226, ô 0244
In Word: Ctrl-Shft-^ then the letter ... but this is word specific and won't work generally in Windows.
Staying with Word, if you want a ë it's CTRL-':'m i.e CTRL-SHIFT ';' then the 'e' or another character. You can get at this generally in Windows with ALT-137, a different scheme from above (see http://www.edu.dudley.gov.uk/ict/software/word/accents.htm). I'll get to investigating the difference between the two schemes.
18/05/2-13
In Welsh the circumflex is known as hirnod 'long sign', acen grom 'crooked accent' and also colloquially as to bach 'little roof'. It lengthens a vowel (a, e, i, o, u, w, y), and is used particularly to differentiate between homographs; e.g. tan and tân, ffon and ffôn, gem and gêm, cyn and cŷn, or gwn and gŵn. I add this as I needed 'ŷ' (the code in this case is 0177) as the standard way to insert a circumflex, Ctrl-Shift-6, then 'y', didn't work, so you type the code then ALT-X. Note this is different from the general Windows approach above.
Note also that while â, ê, î, ô and and û will work with the CTRL-Shift approach ŵ as well as ŷ won't, the code for the former being 0175.
P.S. you can always also Insert-Symbol as well!
Shame it can't all be easier in this day and age!
References
http://en.wikipedia.org/wiki/Circumflex
http://www.fileformat.info/info/unicode/char/177/browsertest.htm
http://www.200words-a-day.com/typing-welsh-characters.html