Output

Web browser

All modern web browsers support UTF-8. But you'll have to let the browser know that you're outputting UTF-8 data, because it is likely that it's standard character encoding is set to something else.
In plain HTML pages add this meta tag in the header:
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
In scripted pages add the meta tag and this header:
"Content-type: text/html; charset=utf-8"
In PHP you would write:
header("Content-type: text/html; charset=utf-8");

Flash

Flash MX and higher expects UTF-8 input, whether you use the XML() or the LoadVars() objects.
Unless someone has put system.useCodepage = true; somewhere in the code.

Mail clients

The Internet Message Format standard (RFC 2822) expects mail to be sent in 7bit US-ASCII encoding. This is without any accents. This standard is extended by the MIME standard, which allows for other character sets and media types.
This chapter is a little harder than the previous ones, but don't panic, every decent scripting language has classes that will handle the details for you: see the MiME::* perl modules or Mail_Mime PHP PEAR class. You just need to know what you're doing, hence all the theory.

Mail subject

According to RFC 2822, mail header fields, including the subject, MUST be composed of printable US-ASCII characters (i.e., characters that have values between 33 and 126, inclusive). So if you want a subject with accents, you must encode it from your original character set to a US-ASCII character set. There are 2 of ways to do this: quoted-printable or base64.

The Quoted-Printable encoding allows any 8bit character to be represented as "=XX", where XX is the hexadecimal value of the character. E.g. "Voilà une message" in the ISO-8859-1 (latin-1) character set is encoded as "Voil=E0=20une=20message".
SPACE characters may be represented as "_". E.g. "Voil=E0_une_message" which is more readable.
"Voilà une message" in the UTF-8 character set is encoded as "Voil=C3=A0_une_message". As you can see the "à" character is encoded as the 2 character sequence "=C3=A0".
Base64 encoding will take 3 characters of the original string and convert them to 4 characters in the range of: A-Z, a-z, 0-9, /. The = is used for padding. E.g. "Voilà une message" is encoded as "Vm9pbOAgdW5lIG1lc3NhZ2U="
I would suggest the Quoted-Printable encoding for subjects that contain mainly ASCII characters. In case the mail client fails to decode the subject correctly, you'll still have an idea what the subject is about. Base64 is unreadable (for most of us).

Now we have an encoded subject, but our mail reader won't know that. So we need to tell it by formatting our subject as follows: "=?" charset "?" encoding "?" encoded-text "?=" , where charset is the original character set and encoding is either "Q" for Quoted-Printable or "B" for Base64.
E.g The subject containing the Quoted-Printable ISO-8859-1 string "Voilà une message", is written as:
Subject: =?ISO-8859-1?Q?Voil=E0_une_message?=
The Base64 version of the ISO-8859-1 string is:
Subject: =?ISO-8859-1?B?Vm9pbOAgdW5lIG1lc3NhZ2U=?=
The Quoted-Printable version of the UTF-8 string is:
Subject: =?UTF-8?Q?Voil=C3=A0_une_message?=
The Base64 version of the UTF-8 string is:
Subject: =?UTF-8?B?Vm9pbMOgIHVuZSBtZXNzYWdl?=

Also note that a single encoded word may not contain more than 75 characters, charset, encoding and delimiters inclusive. If you have a longer subject, read rfc1522 (MIME Part Two). It's great bedtime reading ;-)

Mail Body

In order to use other characters than US-ASCII in the mail body, it must comply with MIME standard. This is easier than the subject. You just add a couple of headers.
For plain text messages, you can output your UTF-8 data without any conversion, after adding these headers:
Mime-Version: 1.0
Content-Type: text/plain; charset=UTF-8;
Content-Transfer-Encoding: 8bit

HTML emails are similar:
Mime-Version: 1.0
Content-Type: text/html; charset=UTF-8;
Content-Transfer-Encoding: 8bit

If (you think) your end user's email client doesn't support UTF-8, you could encode the message body into ISO-8859-1 (Latin-1) and use HTML entities for 'special' characters. The headers would be:
Mime-Version: 1.0
Content-Type: text/html; charset=ISO-8895-1;
Content-Transfer-Encoding: 8bit

How Hotmail handles UTF-8 data is not clear to me. It seems to use a combination of the user's language setting and the e-mail's encoding to determine which character set to use. If your language setting is English, it will display the mail as ISO-8895-1 (Latin-1) or UTF-8, according to the mail's encoding. But if you set your language to Japanese it will display the message as SHIFT_JIS, independent of the mail's encoding.