Is "IF" expensive?

At the very lowest level (in the hardware), yes, ifs are expensive. In order to understand why, you have to understand how pipelines work.

The current instruction to be executed is stored in something typically called the instruction pointer (IP) or program counter (PC); these terms are synonymous, but different terms are used with different architectures. For most instructions, the PC of the next instruction is just the current PC plus the length of the current instruction. For most RISC architectures, instructions are all a constant length, so the PC can be incremented by a constant amount. For CISC architectures such as x86, instructions can be variable-length, so the logic that decodes the instruction has to figure out how long the current instruction is to find the location of the next instruction.

For branch instructions, however, the next instruction to be executed is not the next location after the current instruction. Branches are gotos - they tell the processor where the next instruction is. Branches can either be conditional or unconditional, and the target location can be either fixed or computed.

Conditional vs. unconditional is easy to understand - a conditional branch is only taken if a certain condition holds (such as whether one number equals another); if the branch is not taken, control proceeds to the next instruction after the branch like normal. For unconditional branches, the branch is always taken. Conditional branches show up in if statements and the control tests of for and while loops. Unconditional branches show up in infinite loops, function calls, function returns, break and continue statements, the infamous goto statement, and many more (these lists are far from exhaustive).

The branch target is another important issue. Most branches have a fixed branch target - they go to a specific location in code that is fixed at compile time. This includes if statements, loops of all sorts, regular function calls, and many more. Computed branches compute the target of the branch at runtime. This includes switch statements (sometimes), returning from a function, virtual function calls, and function pointer calls.

So what does this all mean for performance? When the processor sees a branch instruction appear in its pipeline, it needs to figure out how to continue to fill up its pipeline. In order to figure out what instructions come after the branch in the program stream, it needs to know two things: (1) if the branch will be taken and (2) the target of the branch. Figuring this out is called branch prediction, and it's a challenging problem. If the processor guesses correctly, the program continues at full speed. If instead the processor guesses incorrectly, it just spent some time computing the wrong thing. It now has to flush its pipeline and reload it with instructions from the correct execution path. Bottom line: a big performance hit.

Thus, the reason why if statements are expensive is due to branch mispredictions. This is only at the lowest level. If you're writing high-level code, you don't need to worry about these details at all. You should only care about this if you're writing extremely performance-critical code in C or assembly. If that is the case, writing branch-free code can often be superior to code that branches, even if several more instructions are needed. There are some cool bit-twiddling tricks you can do to compute things such as abs(), min(), and max() without branching.

"Expensive" is a very relative term, especially with relationship to an "if" statement since you also have to take into the account the cost of the condition. That could range anywhere from a few short cpu instructions to testing the result of a function that calls out to a remote database.

I wouldn't worry about it. Unless you're doing embedded programming you probably shouldn't be concerned about the cost of "if" at all. For most programmers it's just not going to ever be the driving factor in your app's performance.

Branches, especially on RISC architecture microprocessors, are some of the most expensive instructions. This is because on many architectures, the compiler predicts which path of execution will be taken most likely and puts those instructions next in the executable, so they'll already be in the CPU cache when the branch happens. If the branch goes the other way, it has to go back out to main memory and fetch the new instructions -- that's fairly expensive. On many RISC architectures, all instructions are one cycle except for branch (which is often 2 cycles). We're not talking about a major cost here, so don't worry about it. Also, the compiler will optimize better than you do 99% of the time :) One of the really awesome things about the EPIC architecture (Itanium is an example) is that it caches (and begins processing) instructions from both sides of the branch, then discards the set it doesn't need once the outcome of the branch is known. This saves the extra memory access of a typical architecture in the event that it branches along the unpredicted path.

Check out the article Better Performance Through Branch Elimination on Cell Performance. Another fun one is this post about branchless selections on the Real Time Collision Detection Blog.

In addition to the excellent answers already posted in response to this question, I'd like to put in a reminder that although "if" statements are considered expensive low-level operations, trying to utilize branch-free programming techniques in a higher level environment, such as a scripting language or a business logic layer (regardless of language), may be ridiculously inappropriate.

The vast majority of the time, programs should be written for clarity first and optimized for performance second. There are numerous problem domains where performance is paramount, but the simple fact is that most developers are not writing modules for use deep in the core of a rendering engine or a high performance fluid dynamics simulation that runs for weeks on end. When the top priority is for your solution to "just work" the last thing on your mind should be whether or not you can save on the overhead of a conditional statement in your code.