There is a lot of old information on the web about the differences between NTSC and PAL television systems. Most of this information says that you cannot use a US TV in Europe because NTSC and PAL are not compatible. Now that the world has gone to digital TV, cable, and internet based streaming are PAL and NTSC things of the past. As long as a TV can handle the voltage, potentially with the aid of a transformer, can you use it in any country? Do you have to worry about the voltage frequency (e.g., 50/60 Hz difference between the US and most of Europe)? How do DVD and Blue-ray fit into this?
With the advent of Digital HD TV the difference between NTSC and PAL is practically limited to the framerate of the display which is 23,975p/30p/60i on NTSC and 25p/50i on PAL standards. Modern, digital television sets will have no issues with any of them. The voltage frequency is also not an issue, as the digital decoder is running on DC, so the frequency won't matter unless the AC/DC converter cannot handle it (which should be pretty rare). This assumes you are either only using digital TV (like DVB-T / DVB-C), or using a set-top box that connects digitally to your TV (for example with an HDMI cable)
If you still want to use analog connections the issue might be a bit more problematic, as the analog signal is very different on PAL and NTSC, making it not possible to mix them. You have to consult the manual of your TV whether it supports both standards, or not. As a rule of thumb TVs sold in Europe in this century usually support both PAL and NTSC standards (sometimes also SECAM), but TVs sold in the US might not support PAL. Also if you want to connect a DVD player or a set top box with an analog type connection (like a SCART, RCA or a Coaxial cable) you have to make sure that they run on the same standard, and that they both support the same sets of connectors (for example SCART connectors are not that common on non-European boxes). If they do support multiple standards then also note they might not be able to autodetect the signal, so you should consult the manual on how to switch them if needed.
Don't forget though that aerial analog TV is phased out in Europe in favor of DVB-T and DVB-T2, both digital standards.
@SztupY did a good job except for the last question, which I will address:
How do DVD and Blue-ray fit into this?
DVDs (and possibly Blu-Rays) are still encoded using either NTSC or PAL, but any modern DVD player (and likely any old one) will convert to your TV's expected input. So even if you're playing a British DVD on a US player, you will have no problem watching it on your US TV.
The bigger problem with DVDs and Blu-Rays is not PAL vs. NTSC, but their region encoding. Most commercial DVD/BRs are encrypted so that they can only be played on a player from a specific region. There are far more DVD regions than Blu-Ray regions, making this generally a more complicated problem for DVDs than for Blu-Rays, but in your case, the UK and the US are in different regions on both systems, so this could well be an issue for you.
If you bring your DVD/BR player with you from the UK to the US, you will be able to watch your UK media without a problem on your US TV, but you will also need a US DVD/BR player to watch any media you purchase in the US.
You can also buy multi-region or region-free DVD players, although they are more expensive (as they must be licensed for multiple regions).
Most US HDTVs nowadays I believe do support PAL, like my 16:9 Vizio, but through the RF port the two are still incompatible (because it's fully analog like someone up there said, you can't mix the two in analog). Although if that's true then things like composite and component shouldn't work either but they do, so eh, whatever XD