There is no risk to this approach if the deposits are fully insured and there is no fine print that you are unaware of. Unfortunately, sometimes there is fine print and you have to decide whether the cash bonus is still worth it.
For example, Chase Bank (U.S.) was (is?) offering a $500 bonus for a $15,000 deposit for 3 months. That's 13+ pct annualized which is good. The fine print catch was that you had to keep the account open for 6 months and in order to avoid monthly fees, you had to maintain a balance of $1,500. So that drops the annualized rate about a percent but the Yield is still good for fixed income. At the end of the first 3 months, you withdraw $14,000 ($13,500 plus the cash bonus). and move on to the next opportunity otherwise you may halve your Yield.
I have a friend who does these regularly. She just finished one with HSBC which provided a $200 bonus for a $1,500 deposit and at 3 months, she withdrew all but the $25 minimum which has to remain for another 3 months. She also did one at Fifth Third Bank which offers $200 for a 60 day deposit of $500 but the fine print required $1,500 deposit (or 10 credit card purchases if you have their credit card) in order to avoid monthly fees. That's better than 50% Yield.
Suggestions of opportunity loss are silly. This is fixed income money, If you want this money invested then invest it and there are no guarantees that invested money will do better. But all of that is a different story. This approach for fixed income money bumps Yield up significantly.
If you're a millionaire, this is might be chump change (g). If you're young and you want some free money, go for it!