I'm thinking about becoming a data analyst, and I'm wondering if programming knowledge is a must for this. I'm fairly strong with maths, but I have very little programming experience. Do all data analysts have strong programming skills (R, SAS, SQL, Python, etc.), or can it vary depending on the type of data analyst you are?
I would say you don't need to already have lots of programming experience, but being generally mathematically and computer-literate is important.
If you've literally never programmed a computer before, then dig up a basic online R or python tutorial. As to which one, depends on the industry you'll be working in. Tech companies tend to use python, elsewhere R might be slightly more prevalent.
There are various "drag-and-drop" software "solutions" that don't in theory need programming, but in most real-life applications you'll find that there's functionality you need that they don't have, or you need to pre- or post-process your data in some way, and you'll have to resort to R/python/SAS/... to get that sorted out.
You'll find that you are most likely able to learn the coding skills you need on the job, as long as you have just a little experience with writing code.
Well, it is quite hard to do data science without using the computer. Unless you can do Random Forests by hand :) But if you mean raw programming, then anything you will be using (in 'everyday' DS) is already implemented in R, Python etc.
Regarding the skills, I think R is the best choice - very intuitive, made to be easy to use, although at the expense of speed. Python is becoming the new standard but is script language and takes little more to learn. There is also Eviews for instance that is not really programming at all and is straightforward to use.