There’s a great discussion going on on the IXDA mailing list about what we call mobile phones (and what we call sending SMS messages) in different countries. I’m trying to summarize here, please leave a comment with info on your country and also note where this list may be wrong:
- USA: Cellphone or cell, texting.
- China: “Handy phone” (?)
- Iran: mobile. (landlines are called “telephone”).
- Spain: "teléfono móvil" or "móvil".
- Denmark: mobile phone.
- UK: mobile or mobile phone.
- Philipines: cellphone.
- New Zealand: “mobile” (but cellphone is also used).
- India: mobile. Telephone or landline for a landline.
- Korea: “handphone”
- Japan: keita.
- Dutch (Netherlands): mobiele telefoon.
- Dutch (Belgium): GSM.
- France: "téléphone portable" or "portable" but since "portable" is used for laptop too some people call them "mobile".
- Germany: handy http://de.wikipedia.org/wiki/Handy
- Indonesia, they call it hand phone or simply abbreviated as "hp" pronounced "ha-pe". "*Ha*" as if in *ha*m and "*pe*" as if in*Pe*psi. In terms of texting, they use "SMS".
- Turkey: "pocket phone" ("cep telefonu")?
In general, “text message” is more widely understood than “SMS”.
I also created a Google survey, I’ll open up the results. Fill in the form about what phones are called in your country here.
Peter Van Dijck 
In the US, everything gets shortened, so the word “text” functions as both a noun or verb:
“I’ll send a text” or “text me your cel”
Hi Peter, thanks for this – I was the original poster on the IxDA forum, so you are saving me the task of reporting back!
I’ve worked for mobile phone carriers in Australia and Asia and mostly Australia uses “mobile phone”, “text message” or “SMS” are used and recognised. In Singapore it is “mobile” and in most of indochina it is “Handyphone” but that started as a brand and has become generic.
In Sweden: “Mobil telefon” or just “mobil”
We call it “ceb” in North Cyprus or as in Sweden just “mobil” :)
Info for Japan is incorrect. Keitai Denwa (携帯電話) is the formal name. Keitai（ケータイ or 携帯) is the slang.
Note that this term does NOT include mobile phones using PHS (Personal Handyphone System), that were popular in the 90s. Fortunately for localizers, PHS phones and their associated slang (ピッチ which can be spelled “picchy”) are largely a historical footnote nowadays.