There are many tutorials over the web regarding this problem but unfortunately it is not always the same for everybody.

In my case I have tried all the links below unsuccessfully (for you it might work):

https://support.apple.com/en-us/HT201349
http://www.idownloadblog.com/2014/05/14/how-to-remove-a-phone-number-from-imessage/
http://www.igeeksblog.com/fix-imessage-waiting-for-activation/

also you can try more:
https://duckduckgo.com/?q=imessage+waiting+for+activation&t=osx

In my case, there was a problem with normal SMS and because of that, the phone was unable to send the messages to apple servers in order to activate the iMessages.

So before even trying to activate iMessages and Facetime, try to send a simple text message (sms) and if it fails, fix it before moving forward.

a. if you have an older phone, go to text settings and see if you have the correct number for sending sms.

b. if you have a smartphone and this setting is not available, call this number to check the number: *#5005*7672#
If is incorrect, reset it by calling: ##5005*7672#
And add a new one: **5005*7672*+407xxxxxxxxx#

The text call number you can find it by contacting your operator (or by visiting their websites).
For Vodafone they are as follows:
Subscribers (also Vodafone Office): +40722004000
Prepay: +40722006000.

= iPhone Codes =

Here will be a full table of commands supported by iPhone
using the phone keyboard.
Any command can be preceded by *#, ** or ##.

*# is INTERROGATION.
** is SETUP.
## is CANCEL / DELETE.

*#5005*78283# This dumps a baseband log in /Library/Logs/Baseband/ - Note 1
**5005*78283# This dumps a baseband log in /Library/Logs/Baseband/ - Note 1
##5005*78283# This dumps a baseband log in /Library/Logs/Baseband/ - Note 1
*#5005*62# "Error performing request - No Network Service" - Note 2
*#5005*62255# "Error performing request - No Network Service" - Note 2
*#5005*87223# "Error performing request - No Network Service" - Note 2
*#5005*86# Displays the Voice Mail dial-in number.
**5005*86*VOICEMAIL# Sets the Voice Mail number to VOICEMAIL (international format).
##5005*86# Erases the Voice Mail number from phone.
*#5005*7672# Display the SMSC Setting.
**5005*7672*SMSCNUMBER# Sets the SMSC to SMSCNUMBER (international format).
##5005*7672# Erases the SMSC number from phone.
*#5005*22# "Error performing request - No Network Service" - Note 2
**5005*22# Unknown. Displays "Please wait"; returns to dialpad - Note 2
##5005*22# Unknown. Displays "Please wait"; returns to dialpad - Note 2
*#5005*5264# This reads LANG and tells you the "actual language" (en).
*#5005# "Error performing request - No Network Service" - Note 2
##5005*22*12345678# Function unknown, displays "please wait"...; power-off to exit.

'
Note 1: It may be necessary to change the prefix from the set of (*#, **, ##) to
initiate a new log dump. The logs are not "tail" able, since this is a single
dump, with no additional data written. So far, these logs appear to always
remain the same size. Logfiles are stamped with the current date.

Note 2: These tests were performed with a stock phone on the AT&T network. It is
possible that these errors represent debugging features that are only
available on a special debug cellular base-station (CONJECTURE only!)'