I was just reading another explanation of the halting problem, and it got me thinking all the problems I've seen that are given as examples involve infinite sequences. But I never use infinite sequences in my programs - they take too long. All the real world applications have lower and upper bounds. Even reals aren't truly reals - they are approximations stored as 32/64 bits etc. 

So the question is, is there a subset of programs that can be determined if they halt? Is it good enough for most programs. Can I build a set of language constructs that I can determine the 'haltability' of a program. I'm sure this has been studied somewhere before so any pointers would be appreciated. The language wouldn't be turing complete, but is there such a thing as nearly turing complete which is good enough?

Naturally enough such a construct would have to exclude recursion and unbounded while loops, but I can write a program without those easily enough.

Reading from standard input as an example would have to be bounded, but that's easy enough - I'll limit my input to 10,000,000 characters etc, depending on the problem domain.

tia

[Update]

After reading the comments and answers perhaps I should restate my question.

For a given program in which all inputs are bounded can you determine if the program halts. If so what are the constraints of the language and what are the limits of the input set. The maximal set of these constructs would determine a language which can be deduced to halt or not. Is there some study that's been done on this?