LoL is a MOBA. If you're interested in that style of gameplay, I suggest DotA2, It's better.
As for other MMORPGs i'm curious to see what people say, because I don't know of any other ones which have been quite the same as RS. I tried TERA once, but it required specs which my comp couldnt handle. It was good while it lasted tho.
So yea, if you're stuck with what to play, DotA 2 is your answer for now, although it's a MOBA, not an mmo
MOBA: Massive Online Battle Arena
You team up with 4 other players in a 5v5 arena. Every 'match' lasts between 20 minutes and 2 hours, it depends on the gameplay. When you join, you select which hero you want to play for that 'match'. You then play as that hero using their skillset for the duration of the match, to fight against the opponent in a race to take the enemy's Ancient (base). It's great fun once you pass the steep learning curve (yes, very steep but it's worth it!) and I've played it for close to 2 years and am still enjoying it now
GL!
apa
Edit: After playing perhaps 10 matches you will really start to understand what's going on. That's about 7-8 hours gameplay, seems long but it flies past. When you start (and get into your first match), you will have no idea what's going on (this is normal xd). Just play and you will get the hang of it