You can accelerate your own transactions if you want All you need to do is ensure that the fee you enter is around the current price that most people are paying to get their transaction confirmed which is defined here: https://blockchain.info/charts/cost-per-transaction

The only other way to accelerate your transaction is to mine and find blocks yourself and prioritise your transaction in the next block - this is what some of those services do.

I'm not sure if the price to confirm through acceleration is higher than paying the current transaction confirmation fee but you can look at both options and go for the cheaper one.