If you are alone, you have a better chance of finding an unreserved seat than if you travel with someone else.
I bought tickets in the Copenhagen train station the night before a long day trip - outgoing the train was nearly empty, returning (Friday evening of a holiday weekend) the train was packed. I was glad I had seats reserved for myself and my 11 year old son.
On the other hand, I prepurchased tickets from Stockholm to Oslo and for that 6 hour trip, my tickets only cost about $16 for two of us including seat reservations. So cheap that I worried that I had done something wrong and they would be no good, but all was well and that train was also packed with people on a Monday.
To save money, you might try to buy ahead (the Copenhagen purchased tickets were very, very expensive for train tickets), but I searched ahead, and I never saw a good deal for those. Perhaps only Sweden offers the great pre-purchase deals.