Thanks for the report!
- If you can reproduce the crash at will (or you experience this regularly), can you install the "kdepim-dbg" package and post a complete backtrace here? (you can get more information at http://techbase.kde.org/User:DarioAndres/Basic_Guide_about_Crash_Reporting ) Thanks

Application: Kontact (kontact), signal: Segmentation fault
The current source language is "auto; currently c".
[KCrash Handler]
#5  0x00007fa14078be59 in QObjectPrivate::deleteChildren (this=0x3341fe0) at kernel/qobject.cpp:1847
#6  0x00007fa1410ec4f3 in ~QWidget (this=0x33636c0, __in_chrg=<value optimized out>) at kernel/qwidget.cpp:1367
#7  0x00007fa14078be5c in QObjectPrivate::deleteChildren (this=0x3329390) at kernel/qobject.cpp:1847
#8  0x00007fa1410ec993 in ~QWidget (this=0x2054880, __in_chrg=<value optimized out>) at kernel/qwidget.cpp:1367
#9  0x00007fa1414ab728 in ~QSplitter (this=0x2054880, __in_chrg=<value optimized out>) at widgets/qsplitter.cpp:1008
#10 0x00007fa14078be5c in QObjectPrivate::deleteChildren (this=0x348dbb0) at kernel/qobject.cpp:1847
#11 0x00007fa1410ec4f3 in ~QWidget (this=0x33497d0, __in_chrg=<value optimized out>) at kernel/qwidget.cpp:1367
#12 0x00007fa14078be5c in QObjectPrivate::deleteChildren (this=0x3350620) at kernel/qobject.cpp:1847
#13 0x00007fa1410ec993 in ~QWidget (this=0x3415e40, __in_chrg=<value optimized out>) at kernel/qwidget.cpp:1367
#14 0x00007fa141daa515 in ~KMainWindow (this=0x3415e40, __in_chrg=<value optimized out>) at ../../kdeui/widgets/kmainwindow.cpp:474
#15 0x00007fa12ae4bd25 in ~SecondaryWindow (this=0x2279470, __vtt_parm=<value optimized out>, __in_chrg=<value optimized out>) at ../../kmail/secondarywindow.cpp:56
#16 0x00007fa12abe2f4c in ~Composer (this=0x2279470, __vtt_parm=<value optimized out>, __in_chrg=<value optimized out>) at ../../kmail/composer.h:42
#17 0x00007fa12abdc643 in KMComposeWin (this=0x3415e40, aMsg=<value optimized out>, id=13311104, __in_chrg=<value optimized out>, __vtt_parm=<value optimized out>) at ../../kmail/kmcomposewin.cpp:382
#18 0x00007fa12abdcb44 in KMComposeWin::create (msg=0x2e23b80, identitiy=1002118501) at ../../kmail/kmcomposewin.cpp:140
#19 0x00007fa12ad10d7d in KMKernel::newMessage (this=<value optimized out>, to=<value optimized out>, cc=..., bcc=<value optimized out>, hidden=<value optimized out>, useFolderId=true, 
    _attachURL=...) at ../../kmail/kmkernel.cpp:694
#20 0x00007fa12af752ee in KmailAdaptor::newMessage (this=0xc97670, _c=<value optimized out>, _id=<value optimized out>, _a=0x7fff5505e600) at kmailadaptor.cpp:135
#21 KmailAdaptor::qt_metacall (this=0xc97670, _c=<value optimized out>, _id=<value optimized out>, _a=0x7fff5505e600) at kmailadaptor.moc:255
#22 0x00007fa13e8adad4 in QDBusConnectionPrivate::deliverCall (this=<value optimized out>, object=<value optimized out>, msg=<value optimized out>, metaTypes=..., slotIdx=<value optimized out>)
    at qdbusintegrator.cpp:891
#23 0x00007fa13e8aec69 in QDBusConnectionPrivate::activateCall (this=<value optimized out>, object=0xc97670, flags=273, msg=...) at qdbusintegrator.cpp:796
#24 0x00007fa13e8af547 in QDBusConnectionPrivate::activateObject (this=<value optimized out>, node=..., msg=<value optimized out>, pathStartPos=<value optimized out>) at qdbusintegrator.cpp:1347
#25 0x00007fa13e8aff11 in QDBusConnectionPrivate::handleObjectCall (this=<value optimized out>, msg=<value optimized out>) at qdbusintegrator.cpp:1443
#26 0x00007fa13e8b0305 in QDBusConnectionPrivate::handleMessage (this=<value optimized out>, amsg=...) at qdbusintegrator.cpp:535
#27 0x00007fa13e8b05dd in QDBusConnectionPrivate::sendWithReplyLocal (this=0x6bda50, message=...) at qdbusintegrator.cpp:1797
#28 0x00007fa13e8b13bb in QDBusConnectionPrivate::sendWithReplyAsync (this=0x6bda50, message=..., timeout=<value optimized out>) at qdbusintegrator.cpp:1832
#29 0x00007fa13e89a5d0 in QDBusConnection::asyncCall (this=<value optimized out>, message=..., timeout=0) at qdbusconnection.cpp:542
#30 0x00007fa13e8b8efb in QDBusAbstractInterface::asyncCallWithArgumentList (this=<value optimized out>, method=..., args=<value optimized out>) at qdbusabstractinterface.cpp:430
#31 0x00007fa12c06b26e in OrgKdeKmailKmailInterface::newMessage (this=<value optimized out>, to=<value optimized out>) at ./kmailinterface.h:148
#32 KMailPlugin::openComposer (this=<value optimized out>, to=<value optimized out>) at ../../../../kontact/plugins/kmail/kmail_plugin.cpp:130
#33 0x00007fa12c06b3ed in KMailPlugin::slotNewMail (this=0x2279470) at ../../../../kontact/plugins/kmail/kmail_plugin.cpp:136
#34 0x00007fa12c06b440 in KMailPlugin::qt_metacall (this=0xa6b070, _c=QMetaObject::InvokeMetaMethod, _id=<value optimized out>, _a=<value optimized out>) at ./kmail_plugin.moc:69
#35 0x00007fa140792ddc in QMetaObject::activate (sender=0xa4b080, from_signal_index=<value optimized out>, to_signal_index=<value optimized out>, argv=0x0) at kernel/qobject.cpp:3113
#36 0x00007fa14109c0a7 in QAction::triggered (this=0x2279470, _t1=false) at .moc/release-shared/moc_qaction.cpp:236
#37 0x00007fa14109d4ef in QAction::activate (this=0xa4b080, event=<value optimized out>) at kernel/qaction.cpp:1160
#38 0x00007fa142650153 in Kontact::MainWindow::qt_metacall (this=0x6dcfe0, _c=QMetaObject::InvokeMetaMethod, _id=<value optimized out>, _a=0x7fff5505f4f0) at ./mainwindow.moc:115
#39 0x00007fa140792ddc in QMetaObject::activate (sender=0xa4cc30, from_signal_index=<value optimized out>, to_signal_index=<value optimized out>, argv=0x0) at kernel/qobject.cpp:3113
#40 0x00007fa14109c0a7 in QAction::triggered (this=0x2279470, _t1=false) at .moc/release-shared/moc_qaction.cpp:236
#41 0x00007fa14109d4ef in QAction::activate (this=0xa4cc30, event=<value optimized out>) at kernel/qaction.cpp:1160
#42 0x00007fa141406fea in QAbstractButtonPrivate::click (this=0xa19aa0) at widgets/qabstractbutton.cpp:525
#43 0x00007fa141407275 in QAbstractButton::mouseReleaseEvent (this=0xa3e200, e=0x7fff5505fc20) at widgets/qabstractbutton.cpp:1115
#44 0x00007fa1414d5cba in QToolButton::mouseReleaseEvent (this=0x2279470, e=0x0) at widgets/qtoolbutton.cpp:709
#45 0x00007fa1410f09c0 in QWidget::event (this=0xa3e200, event=0x7fff5505fc20) at kernel/qwidget.cpp:7549
#46 0x00007fa1410a1efc in QApplicationPrivate::notify_helper (this=0x6cd3c0, receiver=0xa3e200, e=0x7fff5505fc20) at kernel/qapplication.cpp:4056
#47 0x00007fa1410a9011 in QApplication::notify (this=<value optimized out>, receiver=0xa3e200, e=0x7fff5505fc20) at kernel/qapplication.cpp:3758
#48 0x00007fa141cd8e56 in KApplication::notify (this=0x7fff55061b40, receiver=0xa3e200, event=0x7fff5505fc20) at ../../kdeui/kernel/kapplication.cpp:302
#49 0x00007fa14077dc2c in QCoreApplication::notifyInternal (this=0x7fff55061b40, receiver=0xa3e200, event=0x7fff5505fc20) at kernel/qcoreapplication.cpp:610
#50 0x00007fa1410a88e0 in QCoreApplication::sendSpontaneousEvent (receiver=0xa3e200, event=0x7fff5505fc20, alienWidget=0xa3e200, nativeWidget=0x6dcfe0, buttonDown=<value optimized out>, 
    lastMouseReceiver=<value optimized out>) at ../../include/QtCore/../../src/corelib/kernel/qcoreapplication.h:216
#51 QApplicationPrivate::sendMouseEvent (receiver=0xa3e200, event=0x7fff5505fc20, alienWidget=0xa3e200, nativeWidget=0x6dcfe0, buttonDown=<value optimized out>, 
    lastMouseReceiver=<value optimized out>) at kernel/qapplication.cpp:2924
#52 0x00007fa14110ea0e in QETWidget::translateMouseEvent (this=0x6dcfe0, event=<value optimized out>) at kernel/qapplication_x11.cpp:4409
#53 0x00007fa14110daa9 in QApplication::x11ProcessEvent (this=<value optimized out>, event=0x7fff55061750) at kernel/qapplication_x11.cpp:3550
#54 0x00007fa141136d0c in x11EventSourceDispatch (s=<value optimized out>, callback=<value optimized out>, user_data=<value optimized out>) at kernel/qguieventdispatcher_glib.cpp:146
#55 0x00007fa139ff7bce in g_main_context_dispatch () from /lib/libglib-2.0.so.0
#56 0x00007fa139ffb598 in ?? () from /lib/libglib-2.0.so.0
#57 0x00007fa139ffb6c0 in g_main_context_iteration () from /lib/libglib-2.0.so.0
#58 0x00007fa1407a61a6 in QEventDispatcherGlib::processEvents (this=0x69fcb0, flags=<value optimized out>) at kernel/qeventdispatcher_glib.cpp:327
#59 0x00007fa1411364be in QGuiEventDispatcherGlib::processEvents (this=0x2279470, flags=<value optimized out>) at kernel/qguieventdispatcher_glib.cpp:202
#60 0x00007fa14077c532 in QEventLoop::processEvents (this=<value optimized out>, flags=) at kernel/qeventloop.cpp:149
#61 0x00007fa14077c904 in QEventLoop::exec (this=0x7fff55061a80, flags=) at kernel/qeventloop.cpp:201
#62 0x00007fa14077eab9 in QCoreApplication::exec () at kernel/qcoreapplication.cpp:888
#63 0x0000000000403f47 in main (argc=<value optimized out>, argv=<value optimized out>) at ../../../kontact/src/main.cpp:218

The above is the backtrace after I installed kdepim-dbg. 
I can reproduce the bug at will:
Kontact/Kmail *always* crash when I click "New Message" 
(or Reply or Forward; note that "New Event" or "New To-Do" 
work perfectly fine).

In the meantime I tried reinstalling most of KDE, but no success;
the error also appears (exactly the same) when I either rename the
config files/folders or create a new user and start contact there.

I posted about this problem in kubuntuforums:
http://kubuntuforums.net/forums/index.php?topic=3109384.0

*Kontact/Kmail, not contact (typo)

*** Bug 221570 has been marked as a duplicate of this bug. ***

Andre: Can you check whether https://bugs.kde.org/show_bug.cgi?id=154373#c10 helps ?

I cannot reproduce this issue with kdepim > 4.7.1.

Feel free to reopen this report is you can reproduce this issue with a recent kontact version.