Text messages from my iPhone to my friend's Android phone do not stay in the 160 characters as sent. Sometimes they appear as two or three separate texts when they are received.
This is normal functionality and has been present on the original iPhone OS on the very first iPhone back in 2007.
What you are seeing is that the iPhone is allowing you to send messages that are longer than the SMS limit, and when you do that it automatically splits the message into the number of SMS messages required to send your message.
If your recipient has an iPhone, they just see the original un-split message as the iPhone puts it back together for the recipient. Other devices, such as your friend's Android device, just show the discrete SMS messages in the order they were sent.
The problem is someone refusing to support Concatenated SMS, as @Andrew Ferrier noted. in a comment on Stu's answer. The spec makes for very dense, acronym-rich reading.
However, there's a section that's relatively readable, which reads:
3.8.3 Text concatenation
If the concatenation mechanism described in subclause 220.127.116.11.1 is not supported by the transmitting or receiving entity, the following textual concatenation mechanism may be used. The first message is ended with a + sign, and each subsequent message start and end with + signs until the final message which starts with a + sign but does not end with a + sign.
<message1>+ +<message2>+ +<message3>
Any header fields placed on the front of an MO or MT message are not added to the second and subsequent messages. This provides a simple mechanism which is completely backward compatible. There is no indication of the number of messages and should a message be lost by the system or arrive out of sequence then the original message cannot be reconstructed. Therefore, wherever possible the concatenation mechanism specified in sub clause 18.104.22.168.1 should be used instead.
Since the '+' characters would be apparent if the receiver didn't support the simple coding but the sender did, it's clear that this simple mechanism is not supported by Apple.
I gave up/lost interest in deciphering the spec before figuring out who supports or doesn't support 22.214.171.124.1 but it doesn't matter too much to me; the blame falls on Apple for not supporting the simple fallback scheme.