I just got my first Android phone. The ZTE Score which runs on Android 2.3.4.. I'm curious if I can update to a newer Android os, or if I'm stuck with 2.3.4..
As I stated in the Comments, version 2.3.4 is the latest version for phones. Versions 3.0, 3.1, and 3.2 are all for tablet devices. Version 4.0 will be released on the Galaxy Nexus sometime this month. Version 4.0 (code named Ice Cream Sandwich) was designed to run on both phones and tablets which may clear up the confusion surrounding the numbered releases.
Though Google controls the Android operating system and when it gets released, it is up to the manufacturers to decide whether to put it on their devices. Some companies, like HTC and Motorola, actually rewrite pieces of Android with their own special features, like HTC Sense and Motorola Blur. The companies have the choice to push out an update or not. Some of those companies have come out with plans to update their phones to 4.0.
ZTE has not announced (as of a couple weeks ago) any plans to upgrade their phones to 4.0 but there's no doubts they won't.
The second option is to wait until Google releases the code for 4.0. Once they do this, the Android community (like XDA) will work on a ROM of the operating system which you would then be able to install on your device manually. Doing so is not an easy process and involves dedication and a free weekend. If you consider this route, you should also do a little research to make sure doing so won't "brick" your phone or cause side effects with your service provider. However, it will provide the most clean and pure Android experience you can get.
EDIT: As @eldarerathis pointed out in the comments, Google did release a version of Gingerbread numbered 2.3.7 but it is only to support there Google Wallet product which at this time is only supported on Nexus devices or devices with NFC. If you'd like to build this version yourself and install it on your device, you can download the Android source code and build it yourself. There are instructions on how to do this at the site. However, I would strongly recommend waiting until 4.0 (Ice Cream Sandwich) is released. For documentary purposes, I will update this answer upon release of 4.0.