This work introduces several budget-aware algorithms to deploy scientific workflows on IaaS Cloud platforms, where users can request Virtual Machines (VMs) of different types, each with specific cost and speed parameters. We use a realistic application/platform model with stochastic task weights, and VMs communicating through a datacenter. We extend two well-known algorithms, HEFT and Min-Min, and make scheduling decisions based upon machine availability and available budget. During the mapping process, the budget-aware algorithms make conservative assumptions to avoid exceeding the initial budget; we further improve our results with refined versions that aim at rescheduling some tasks onto faster VMs, thereby spending any budget fraction leftover by the first allocation. These refined variants are much more time-consuming than the former algorithms, so there is a trade-off to find in terms of scalability. We report an extensive set of simulations with workflows from the Pegasus benchmark suite. Budget-aware algorithms generally succeed in achieving efficient makespans while enforcing the given budget, and despite the uncertainty in task weights.