tl;dr This is very bad. The patch causes performance degradation, but not patching is worse.
Here's everything I've been able to find so far:
The issue impacts all modern Intel CPUs. (Edit: It's been confirmed that the latest unaffected CPU is the original Pentium.) According to an AMD engineer, "AMD processors are not subject to the types of attacks that the kernel page table isolation feature protects against. The AMD microarchitecture does not allow memory references, including speculative references, that access higher privileged data when running in a lesser privileged mode when that access would result in a page fault." In short, AMD does not have the bug.
If successfully exploited, it could allow any program running on your computer (including a webpage with JavaScript) to access memory used by the operating system, giving it total control over your computer.
There is a patch in the works for both Windows and Linux that protects against this. However, the patch can cause a large impact on performance. It slows down any "syscalls" - function calls where the program talks directly to the operating system. This includes everything from opening files to communicating over the network; it is almost impossible to write a modern program without them.
The performance impact seen depends on the amount of syscalls the application makes. Raw number-crunching applications will see very little performance impact, whereas applications that have to talk to the OS a lot can see a large impact.
Raw numbers are hard to find due to the secretive nature of these patches, but here are some basic benchmark impacts we've seen so far:
Linux, on an i7 6700, calling the getpid syscall 100,000,000 times:
Before the patch: ~3.8 seconds.
After the patch: ~15 seconds.
PostgreSQL, a database application, i7-6820HQ, SELECT 1 benchmark:
Before the patch: 420490.162391 transactions per second
After the patch: 350746.065039 transactions per second
How bad is it? The intel CEO sold 39.2M in stocks last November with averaging price of $44… while considering that Intel CFO Robert Swan reportedly said in a memo seen by The Oregonian that the company aims to boost its market capitalization to $300 billion (implying a share price north of $60) by 2021. Its big enough that the intel CEO is willing take his chances with insider trading charges…
VIDEO EXPLANATION - https://www.youtube.com/watch?v=9xhNY7v1R80
I don't know enough to have an educated opinion but I am very very very concerned. Thankfully, main PC's are running AMDs but I still have 3 laptops that run in Intels and 2 of them are expected to be of a reasonably secure nature.