For what ?
A a lot of IO and networking maybe Java.
For a large reusable and fast app C++.
For a embedded system maybe ASM or C
and so forth ...

and also
writing something in ISO C++ makes your program platform independent.

Not assembly. Use C++.

Unless you are a very, very tallented assembly coder, you won't be faster than C++ And talented or not, development will take 10 times as long if you use assembly.

If you need to have a small section of code in assembly, you'll know this when you come to it, and you'll be able to insert the assembly into the C++ program.

And as was said - don't start with assembly. Write it all in C++ first, and then use assembly if you've profiled your application and you know you absolutly need it (and then profile again, so you know if your assembly is faster or slower).

From your post I suppose that you don't know them, and want to know the differences to be able to choose what language to study. Well, I don't know assembly very well, but I really suggest you to study C++ for the following reasons (supposing that you are going to make common apps, no drivers-embedded-...):

Speed- ASM is potentially faster, because it let you to have control over every single instruction and memory usage. In addition, most compilers aren't able to take full advantage from the lastest CPU intructions (SSE/SSE2 and so on) because, IIRC some of them need a special setup of the code to be fully used (i.e. an instruction can be executed on many vars at the same time). But, and that is very important, compilers generate in most cases a code faster than what everyone but very experts can do, so the only way one can obtain ASM code faster than C++ one is to know ASM (and algorithms) very, very, very well.

Portability- C++ is, as a language, portable. ASM doesn't. That is, plain c++ code can be sucefully compiled on each system whit a standard compliant c++ compiler. Assembly instructions are different from a CPU to another and even from a OS to another there are differences in the programming rules (I mean interface with the OS and other, but I'm not an expert).

Easy to study- ASM is not difficult to study. Some people think that it is actually easer than C++.

Easy to use- Once you know the languages, I think that programming in C++ is a lot easer (and faster) than ASM, expecially for todays applications (like GUIs, net based applications, databases).

C/C++ is in my opinion a must for every programmer. There aren't, always IMHO, other languages as important as C/C++, aven if you will use other languages at work (or for yourself). So my suggestion is: learn C++ anyway, and then go into ASM, if you like.

edit: oh, I waited too much to anwer: others have already said that. So you're gonig to make games: well C++ is what you need (unless you want to spend months for even the simplest one). Quake was made in C (something in QuakeC and something in ASM), quake 2 in C++ (or C? don't remember), so Half Life 1/2 and, actually, most games. The only game made entirely in ASM I'm aware of is Roller Coster (don't know wich one) according to what said on another post in this forum.