The answer is yes, it's possible to have 1MB/Sec download speeds if you're willing to pay extra. Here's why: Data transfer speeds are advertised by internet service providers in mega-bits per second (not mega-Bytes, which is how you've asked the question.) So, for example, Comcast advertises 6 Mbits/sec download which is actually about 0.75 MBytes/sec = 750 KBytes/sec.
It's rare to reach this maximum download rate on a residential line because of all the other people (neighbors) that share the pipe that is feeding your home, as well as limitations based on the download protocol you're using (some protocols are more efficient than others). Using that 6 Mbit Comcast connection, I average between 300 and 400 MBytes/sec downloads.
In reality you should expect your download rates to be about 1/2 the advertised rate. So based on your comment that you get 100-120 KB/sec, I'm guessing you have a DSL line that is rated at 2 Mbits/sec download.
If you really want 1MByte/sec downloads you'll need to purchase a commercial grade internet connection rated at 16 Mbits/sec. This type of service is called "fractional T3" and would require you to pay for fairly expensive up-front installation and equipment costs. Oh, also the service would cost several hundred dollars per month.
Even if you did all this, you're not guaranteed to hit 1MByte/sec download speeds because the sending side (website or ftp site) may not be able to send the data that fast.
So I guess what I'm saying is that 1MByte/s download speed is possible, but because of the expense, you may want to decide if that is really what you need. Can you upgrade your service to 6 or 8 Mbits/second and be happy? Can you switch to a cable service or FIOS provider?
Good Luck!