This is, in fact, a very good question. People should think about security more.
Yes, but it depends what e-mail service you're using. A very few services don't publish your original IP address. The ones that don't (that I know of) are listed here: http://419.freehostia.com/?node=webmail
If you know how to get the header of an e-mail message, you can usually paste it here http://headertool.apelord.com/ and it will tell you what the original IP address is *AND* what city that IP address is. Here's an example, using the header from a message sent to me by my sister in law:
Delivered-To: redacted@gmail.com
Received: by 10.229.214.83 with SMTP id gz19cs88555qcb;
Fri, 16 Apr 2010 15:09:08 -0700 (PDT)
Received: by 10.229.189.212 with SMTP id df20mr1513599qcb.21.1271455748257;
Fri, 16 Apr 2010 15:09:08 -0700 (PDT)
Return-Path:
Received: from forward.a.hostedemail.com (forward.a.hostedemail.com [216.40.42.17])
by mx.google.com with ESMTP id 34si4933123qyk.89.2010.04.16.15.09.07;
Fri, 16 Apr 2010 15:09:07 -0700 (PDT)
Received-SPF: neutral (google.com: 216.40.42.17 is neither permitted nor denied by best guess record for domain of redacted@yahoo.com) client-ip=216.40.42.17;
Authentication-Results: mx.google.com; spf=neutral (google.com: 216.40.42.17 is neither permitted nor denied by best guess record for domain of redacted@yahoo.com) smtp.mail=redacted@yahoo.com; dkim=pass (test mode) header.i=@yahoo.com
Received: from smtpin01.hostedemail.com (smtpin01.a.tucows.com [10.5.16.1])
by ofarelay03.hostedemail.com (Postfix) with SMTP id 7DC6D4609BC
for ; Fri, 16 Apr 2010 22:09:06 +0000 (UTC)
X-Forwarded-For: redacted@gmail.com by Hostedemail
Delivered-To: redacted@gmail.com
X-FDA: 63459103092.01
X-Panda: scanned!
X-Filterd-Recvd-Size: 15974
Received: from web52803.mail.re2.yahoo.com (web52803.mail.re2.yahoo.com [206.190.48.246])
by imf21.hostedemail.com (Postfix) with SMTP
for ; Fri, 16 Apr 2010 22:09:05 +0000 (UTC)
Received: (qmail 65697 invoked by uid 60001); 16 Apr 2010 22:09:05 -0000
DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=yahoo.com; s=s1024; t=1271455745; bh=X4/xYTVsub3uCgLLQer5Ayzi5JY2qAvZOYpgeSKhFzA=; h=Message-ID:X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type; b=zB6Ijwc+kBx3SCB884qaRdSYHJYdGHT0+6xBRQZOA/DmwwxrBbmJ+vMOKLidQDnTn7xz5je3XdrFgYp4JfAGM0wS0ia1YbIqzUuOquE6FuYzL9JVzqFu/mtofLxIRFk17hOoxwjWB6+65WbORc07NWKi5wmUArcDM5I5mWCFO9w=
DomainKey-Signature:a=rsa-sha1; q=dns; c=nofws;
s=s1024; d=yahoo.com;
h=Message-ID:X-YMail-OSG:Received:X-Mailer:Date:From:Subject:To:In-Reply-To:MIME-Version:Content-Type;
b=UuVORXFTNoT/eh8wy8GT0LEOmFHjFIUjhqTEnsRljica0LW1oztW0cHC06Her5x8IDcAoejuht+QhzWSTGZwkXmuAc8MZX0mWomNvxG66rKgPIzQBd5p7vYMnHKfES6JYOYdRWaT3TBv/gJPivhaR+QVaVHo7wEXvalv1foTp68=;
Message-ID: <253145.64490.qm@web52803.mail.re2.yahoo.com>
X-YMail-OSG: WJa_LRUVM1kTdU1VVSz_8Ek_0tBVWGxBW9zFSU1vI_jd4ms
v7iu.rGZX2GypfP23afdF1MOBbqpj7bi06OTPV4MaOSQedKwfS5ClzL_xUwq
3M1lNUc1G9k.g_uPDcdPjrPIqW5CGJSHECeg4Kxug1oIk5oyllUhHRphOGiU
YMTzJ5Mv6HuUA6fnnNs0FsikS51QmOKhVU4WkMRzXPqF6Ax3MErKxal5M9k.
Bkkn2uTOL6CDo19rzsl3ZAcysP.zoV6bgOa9nDBfCqe4_P5qlKxNeo7Vlk.3
aribot6QyK8AQ5hCP5_ej18bm4IgQSHWOmuJhcoSPVkv5x77v6ilE3p4n2pf
suw--
Received: from [206.174.124.47] by web52803.mail.re2.yahoo.com via HTTP; Fri, 16 Apr 2010 15:09:05 PDT
X-Mailer: YahooMailClassic/10.1.9 YahooMailWebService/0.8.100.260964
Date: Fri, 16 Apr 2010 15:09:05 -0700 (PDT)
From: Dana Smith
Subject: Re: Why civil service isn't all peaches and cream
To: "R. Toby Smith"
In-Reply-To:
MIME-Version: 1.0
In this case, the header tool correctly identifies her IP address as 206.174.124.47 in Juneau, Alaska.