Ruby on rails Databases with large volumes of data effect speed?

My question is pretty much in the title but I'm wondering if a large quantity of data with largely effect the speed of a database in ruby on rails in my current case I want to store every users games in one database with a id that references to the user however I feel that if I do this eventually that database will get too big and slow the whole website down so will it not matter or would there be a better way of doing something like this?

Thanks in advance

-Jason Attwood