12AX7 or 12AT7

Yes and no, mostly no. It will plug in and work but it is not designed to be a replacement. The big differences are that the X has about twice as much gain and the T can handle quite a bit more current. So you usually see an X in the early stages to take advantage of it's gain and a T on the output or as a driver since it can source more current. The X also has quite a bit higher plate impedance. All these factors mean that a circuit optimized for the characteristics of the X probably won't sound as good with the T.

If you replace an X with a T, the gain is reduce and it may sound like crap probably but no harm will be done. On the other hand, if a T is being used toward the limits of it's design, replacing it with an X can push the X past it's limits.

OK Herman, but where does 12AU7 fit into the scheme of the 12A.. family?

Check out this URL:
http://thetubestore.com/gainfactor.html

The U has less gain and lower plate impedance than an X or T, about 1/3 the gain of the T and 2/3 of the plate impedance, about 1/5 the gain of the X and about 1/10 the plate impedance. It has about the same current capabilities of the T.

Unless you really understand the characteristics of these tubes and the topology of your circuit you are generally better off sticking with the original tube type.