In DOS 16 bit, I dont remember being able to do that. You could have multiple things that were each 64K (bytes)(because the segment could be adjusted and the offset zeroed) but dont remember if you could cross the boundary with a single array. The flat memory space where you could willy nilly allocate whatever you wanted and reach as deep as you liked into an array didnt happen until we could compile 32 bit DOS programs (on 386 or 486 processors). Perhaps other operating systems and compilers other than microsoft and borland could generate flat arrays greater than 64kbytes. Win16 I dont remember that freedom until win32 hit, perhaps my memory is getting rusty...You were lucky or rich to have a megabyte of memory anyway, a 256kbyte or 512kbyte machine was not unheard of. Your floppy drive had a fraction of a meg to 1.44 meg eventually, and your hard disk if any had a dozen or few meg, so you just didnt compute thing that large that often.
I remember the particular challenge I had learning about DNS when you could download the entire DNS database of all registered domain names on the planet, in fact you had to to put up your own dns server which was almost required at the time to have a web site. That file was 35megabytes, and my hard disk was 100megabytes, plus dos and windows chewing up some of that. Probably had 1 or 2 meg of memory, might have been able to do 32 bit dos programs at the time. Part if it was me wanting to parse the ascii file which I did in multiple passes, but each pass the output had to go to another file, and I had to delete the prior file to have room on the disk for the next file. Two disk controllers on a standard motherboard, one for the hard disk and one for the cdrom drive, here again this stuff wasnt cheap, there were not a lot of spare isa slots if you could afford another hard disk and disk controller card.
There was even the problem of reading 64kbytes with C you passed fread the number of bytes you wanted to read in a 16 bit int, which meant 0 to 65535 not 65536 bytes, and performance dropped dramatically if you didnt read in even sized sectors so you just read 32kbytes at a time to maximize performance, 64k didnt come until well into the dos32 days when you were finally convinced that the value passed to fread was now a 32 bit number and the compiler wasnt going to chop off the upper 16 bits and only use the lower 16 bits (which happened often if you used enough compilers/versions). We are currently suffering similar problems in the 32 bit to 64 transition as we did with the 16 to 32 bit transition. What is most interesting is the code from the folks like me that learned that going from 16 to 32 bit int changed size, but unsigned char and unsigned long did not, so you adapted and rarely used int so that your programs would compile and work for both 16 and 32 bit. (The code from folks from that generation kind of stands out to other folks that also lived through it and used the same trick). But for the 32 to 64 transition it is the other way around and code not refactored to use uint32 type declarations are suffering.
Reading wallyk's answer that just came in, the huge pointer thing that wrapped around does ring a bell, also not always being able to compile for huge. small was the flat memory model we are comfortable with today, and as with today was easy because you didnt have to worry about segments. So it was a desireable to compile for small when you could. You still didnt have a lot of memory or disk or floppy space so you just didnt normally deal with data that large.
And agreeing with another answer, the segment offset thing was 8088/8086 intel. The whole world was not yet dominated by intel, so there were other platforms that just had a flat memory space, or used other tricks perhaps in hardware (outside the processor) to solve the problem. Because of the segment/offset intel was able to ride the 16 bit thing longer than it probably should have. Segment/offset had some cool and interesting things you could do with it, but it was as much a pain as anything else. You either simplified your life and lived in a flat memory space or you constantly worried about segment boundaries.