Many mobile carriers have in place email-to-text "SMS gateways" to enable subscribers to use email to send SMS or MMS text messages. Below is a quick list of US and International carriers and their corresponding email address formats.
To text a "number", just send an email to the following address for the corresponding carrier:
USAAT&T - number@txt.att.net (or: number@mms.att.net)
Google Fi - number@msg.fi.google.com
Verizon - number@vtext.com
T-Mobile - number@tmomail.net
MetroPCS - number@mymetropcs.com
Sprint - number@messaging.sprintpcs.com, number@pm.sprint.com (MMS)
Airfire Mobile number@sms.airfiremobile.com
Alaska Comminications number@msg.acsalaska.com
Ameritech number@paging.acswireless.com
Assurance Wireless number@vmobl.com
Boos Mobile number@sms.myboostmobile.com, number@myboostmobile.com
Cellcom number@cellcom.quiktxt.com
Cleartalk number@sms.cleartalk.us
Cricket number@sms.mycricket.com, number@mms.mycricket.com
Edge Wireless number@sms.edgewireless.com
Hawaiian Telcom Wireless number@hawaii.sprintpcs.com
US Cellular number@email.uscc.net , number@mms.uscc.net
Virgin Mobile number@vmobl.com
InternationalGlobalstar Satellite (international) number@msg.globalstarusa.com
Austria - Api4SMS number@members.api4sms.net
Brazil - Claro number@clarotorpedo.com.br
Bulgara - Globul 35989number@sms.globul.bg
Canada - Aliant number@sms.wirefree.informe.ca
Canada - Bell Mobility/Solo Mobile number@txt.bell.ca, number@txt.bellmobility.ca
Canada - Telus Mobility number@msg.telus.com, number@mms.telusmobility.com (MMS)
Canada - Virgin Mobile number@vmobile.ca
China - China Mobile number@139.com
Germany - E-Plus 0number@smsmail.eplus.de
Germany - T-Mobile number@t-mobile-sms.de
Germany - Vodafone 0number@vodafone-sms.de
UK - AQL number@text.aql.com
UK - Kapow number@kapow.co.uk
India - Airtel number@aircel.co.in, number@airtelap.com, number@airtelkk.com (Karnataka)
India - Idea Cellular number@ideacellular.net
Netherlands - T-Mobile 31number@gin.nl
Puerto Rico - Claro number@vtexto.com
Russia (Beeline) number@sms.beemail.ru
Notes: For some carriers, prepaid SIM customers may not be able to receive SMS/MMS messages using their respective SMS gateways.
If you don't know the mobile carrier of the number you're trying to reach, there are a few websites that provide free carrier lookup online.