The limit here is one of design: each block is currently limited to X MB, each transaction takes Y bytes, and each block is designed to happen every Z minutes; for Bitcoin's current values of 1MB (expected to be raised at some point if the size becomes a limit), something like 1k, and 10 minutes, that works out to 7 transactions per second.
Altcoins which have chosen blocktimes of say 1 minute will be able to do more transactions per second, and ones which lift the 1MB cap likewise.
Altcoins which have chosen blocktimes of say 1 minute will be able to do more transactions per second, and ones which lift the 1MB cap likewise.